Common use of Bibliography Clause in Contracts

Bibliography. [9] Xxxxxxx Xxxxxx and Xxxxx Xxxxxx. Examples of CM curves of genus two defined over the reflex field. LMS J. Comput. Math., 18(1):507– 538, 2015. [10] Xxxxx Xxxxx. Advanced topics in computational number theory, vol- ume 193 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2000. [11] Xxxxx X. Xxx. Primes of the form x2 +ny2. Pure and Applied Math- ematics (Hoboken). Xxxx Xxxxx & Sons, Inc., Hoboken, NJ, second edition, 2013. Xxxxxx, class field theory, and complex multiplication. [12] Xxxxx Xxxxxx. The structure of Galois groups of CM-fields. Trans. Amer. Math. Soc., 283(1):1–32, 1984. [13] Xxxxx Xxxxx et al. Echidna algorithms for algebra and geometry experimentation. xxxx://xxxxxxx.xxxxx.xxxx.xxx.xx/˜xxxxx/ dbs/complex_multiplication2.html. [14] Xxxx X. Xxxxx and Xxxxxxx X. Xxxxxx. Genus 2 curves with complex multiplication. Int. Math. Res. Not. IMRN, (5):1068–1142, 2012. [15] Xxxxx Xxxxxxxxxx. Algebraic geometry. Springer-Verlag, New York- Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. [16] Xxxx Xxxxxxx. Diophantische Analysis und Modulfunktionen. Math. Z., 56:227–253, 1952. [17] Pınar Kılı¸cer. Sage packages for computing (non-biquadratic) quartic fields with CM class number one. xxxx://xxx.xxxx. xxxxxxxxxx.xx/˜kilicerp/codes/, 2015. [18] Pınar Kılı¸cer and Xxxxx Xxxxxx. The CM class number one problem for curves of genus 2. xxxx://xxxxx.xxx/pdf/1511.04869v1.pdf, 2015. [19] Xxxxx Xxxxx and Xxxxxxxx Xxxx. Construction of XX Xxxxxx curves. [20] Xxxxx Xxxx. Complex multiplication, volume 255 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Math- ematical Sciences]. Springer-Verlag, New York, 1983. [21] Xxxxx Xxxx. Algebraic number theory, volume 110 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1994. [22] Xxxxx Xxxx. Algebra, volume 211 of Graduate Texts in Mathematics. Springer-Verlag, New York, third edition, 2002. [23] St´ephane Louboutin. On the class number one problem for nonnor- mal quartic CM-fields. Tohoku Math. J. (2), 46(1):1–12, 1994. [24] St´ephane Louboutin. CM-fields with cyclic ideal class groups of 2-power orders. J. Number Theory, 67(1):1–10, 1997. [25] St´ephane Louboutin. Explicit upper bounds for residues of Dedekind zeta functions and values of L-functions at s = 1, and explicit lower bounds for relative class numbers of CM-fields. Canad. J. Math., 53(6):1194–1222, 2001. [26] St´ephane Louboutin. Explicit lower bounds for residues at s = 1 of Dedekind zeta functions and relative class numbers of CM-fields. Trans. Amer. Math. Soc., 355(8):3079–3098, 2003. [27] St´xxxxxx Xxxxxxxxx, Xxxxxxx Xxxxxxx, and Xxxxxx Xxxxxxx. The class number one problem for some non-abelian normal CM-fields. Trans. Amer. Math. Soc., 349(9):3657–3678, 1997.

Bibliography. [1] Xxxx Xxxxxxxx, Xxxxxxxx Xxxxxxxxx, and Xxxxxxxx Xxxxxxxxxxx. CSI-FiSh: Ef- ficient isogeny based signatures through class group computations. In Asia- crypt (1), volume 11921 of Lecture Notes in Computer Science, pages 227–247. Springer, 2019. xxxxx://xx.xx/2018/485. [2] Xxx Xxxxx, Xxxxxx Xxxxx, and Xxxxxxxxx Xxx. Oblivious pseudorandom func- tions from isogenies. In Asiacrypt (2), volume 12492 of Lecture Notes in Computer Science, pages 520–550. Springer, 2020. xxxxx://xx.xx/2020/1532. [3] Xxxx Xxxxx and Xxxxx Xxxxxxxxxxx. On the computation of quadratic 2-class groups. J. Th´eor. Nombres Bordeaux, 8(2):283–313, 1996. [4] Xxxxxx Xxxxxxxx and Xxxxxx Xxxxx. CSIDH on the surface. In Xxxxxx Xxxx and Xxxx-Xxxxxx Xxxxxxx, editors, PQCrypto 2020, volume 12100 of Lecture Notes in Computer Science, pages 111–129. Springer, 2020. [5] Xxxxxx Xxxxxxxx, Xxx Xxxxx, Xxxxx Xxxxxxxxx, and Xxxxxxxxx Xxxxxxx. A fusion algorithm for solving the hidden shift problem in finite abelian groups. In PQCrypto, volume 12841 of Lecture Notes in Computer Science, pages 133–153. Springer, 2021. xxxxx://xxxxxx.xxxx.xxx/2021/562. [6] Xxxxxx Xxxxxxxx, Xxxxx Xxxxx, Xxxxx Xxxxxxxxxx, Xxxxxx Xxxxx, and Xxxxx Xxxxx. CSIDH: An efficient post-quantum commutative group action. In Asia- crypt 2018 Pt. 3, volume 11274 of Lecture Notes in Computer Science, pages 395–427. Springer, 2018. [7] Xxxxxx Xxxxxxxx, Xxxxxx Xxxxx, and Xxxxxxxx Xxxxxxxxxxx. Rational isogenies from irrational endomorphisms. In Eurocrypt (2), volume 12106 of Lecture Notes in Computer Science, pages 523–548. Springer, 2020. xxxxx://xx.xx/2019/1202. [8] Xxxxxx Xxxxxxxx, Xxxx Xxx´xxxx´a, and Xxxxxxxx Xxxxxxxxxxx. Breaking the de- cisional Xxxxxx-Xxxxxxx problem for class group actions using genus theory. In Crypto (2), volume 12171 of Lectures Notes in Computer Science, pages 92–120. Springer, 2020. xxxxx://xx.xx/2020/151. [9] Xxxxxxx Xxxxxx Xxxxxxxx Xxxxx and Xxxxx XxxxxxXxxxxxxx Xxxxx. Examples of CM curves of genus two defined over the reflex fieldHigher-degree supersingular group actions. LMS J. ComputIn MathCrypt, X. Math. Math.Cryptol. (to appear), 18(1):507– 538, 20152021. xxxxx://xx.xx/2021/955. [10] Xxxxxxxx Xxx`o and Xxxxx Xxxxx. Advanced topics in computational number theoryOrienting supersingular isogeny graphs. Journal of Mathematical Cryptolology, vol- ume 193 of Graduate Texts in Mathematics. Springer-Verlag14(1):414–437, New York, 20002020. [11] Xxxx-Xxxx Xxxxxxxxxx. Hard homogeneous spaces, 2006. Unpublished article, available at xxxxx://xxxxxx.xxxx.xxx/2006/291. [12] Xxxxx X. Xxx. Primes of the form x2 ++ ny2. Pure and Applied Math- ematics (Hoboken). Xxxx Xxxxx & Sons, Inc., Hoboken, NJ, second edition, 2013. Xxxxxx: Fermat, class field theory, and complex multiplication. [12] Xxxxx XxxxxxPure and Applied Mathematics. The structure of Galois groups of CM-fields. Trans. Amer. Math. Soc.Wiley, 283(1):1–32second edition, 19842013. [13] Xxxxx Xxxxx et alXxxxxxxx Xxxxxxx and Xxxx Xx Xxx. Echidna algorithms for algebra and geometry experimentationOn the security of OSIDH. xxxx://xxxxxxx.xxxxx.xxxx.xxx.xx/˜xxxxx/ dbs/complex_multiplication2.htmlIn PKC (1), volume 13177 of Lecture Notes in Computer Science, pages 52–81. Springer, 2022. xxxxx://xx.xx/2021/1681. [14] Xxxx X. Xx Xxx, Xxxxxxx Xxxxxxx de Saint Guilhem, Xxxx Xxxxx Xxxxxxx, P´eter Xx- xxx, Xxxxxxx Xxxxxx, Xxxxxxxxxx Xxxxx, Xxxxxx Xxxxx, and Xxxxxxx X. XxxxxxXxxxxxxx Xxxxxxxxxx. Genus 2 curves with complex multiplicationS´eta: Supersingular encryption from torsion attacks. IntIn Asiacrypt (4), volume 13093 of Lecture Notes in Computer Science, pages 249–278. MathSpringer, 2021. Res. Not. IMRN, (5):1068–1142, 2012xxxxx://xx.xx/2019/1291. [15] Xxxxx XxxxxxxxxxXxxx Xx Xxx and Xxxxxxx Xxxxx. Algebraic geometryThreshold schemes from isogeny assumptions. In PKC (2), volume 12111 of Lecture Notes in Computer Science, pages 187–212. Springer-Verlag, New York- Heidelberg, 19772020. Graduate Texts in Mathematics, No. 52xxxxx://xx.xx/2019/1288. [16] Xxxx Xxxxx Xxxxxxx, P´eter Xxxxx, Xxxxx-Xxxxxxx Merz, and Xxx Xx Xx. Diophantische Analysis und ModulfunktionenOn the isogeny problem with torsion point information. MathIn PKC (1), volume 13177 of Lecture Notes in Computer Science, pages 142–161. Z.Springer, 56:227–253, 19522022. https: //xx.xx/0000/000. [17] Pınar Kılı¸cerXxxxxx X. Xxxxxxxxx, Xxxxxxxxxx Xxxxx, Xxxxx Xxxxx, and Xxx Xx Xx. Sage packages for computing On the security of supersingular isogeny cryptosystems. In Asiacrypt (non-biquadratic) quartic fields with CM class number one1), volume 10031 of Lecture Notes in Computer Science, pages 63–91. xxxx://xxx.xxxxSpringer, 2016. xxxxxxxxxx.xx/˜kilicerp/codes/, 2015https:// xx.xx/0000/000. [18] Pınar Kılı¸cer Xxxxx Xxx and Xxxxx XxxxxxXxxx Xx Xxx. The CM class number one problem for curves Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. In PQCrypto, volume 7071 of genus 2Lecture Notes in Computer Science, pages 19–34. xxxx://xxxxx.xxx/pdf/1511.04869v1.pdfSpringer, 20152011. xxxxx://xx.xx/2011/506. [19] Xxxxx Xxxxx X. Xxxxxxx and Xxxxxxxx XxxxXxxxxxxxxxx Xxxxx. Construction of XX Xxxxxx curvesFast polynomial factorization and modular composition. In IEEE FOCS 2008, pages 146–155, 2008. xxxx://xxxxx. xxx.xxxxxxx.xxx/~xxxxx/xxxxxx/XX00-xxxxx.xxx. [20] Xxxxx XxxxYi-Fu Xxx, Xxxxxx X. Xxxxxxxxx, and Xxxxxxx Xxxxxxx de Saint Guilhem. Complex multiplicationCom- pact, efficient and UC-secure isogeny-based oblivious transfer. In Eurocrypt (1), volume 255 12696 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Math- ematical Sciences]Lecture Notes in Computer Science, pages 213–241. Springer-Verlag, New York, 19832021. xxxxx://xx.xx/2020/1012. [21] Xxxxx X. Xxxxx. Complex multiplication (v0.10), 2020. xxxxx://xxx.xxxxxx. org/math/CourseNotes/cm.html. [22] Xxxxxxx Xxxxx. On oriented supersingular elliptic curves. Finite Fields Appl., 69:Paper No. 101777, 18, 2021. [23] Xxxxxxx Xxxxx. Probabilistic algorithms in finite fields. SIAM J. Com- put., 9(2):273–280, 1980. xxxx://xxxxxxxxxxxx.xxxxx.xxx.xxx/lcs/pubs/ pdf/MIT-LCS-TR-213.pdf. [24] Xxxxxxxxx Xxxxxxxxxx and Xxxxx Xxxxxxxxx. Public-key cryptosystem based on isogenies. IACR Cryptology ePrint Archive 2006/145, 2006. xxxxx://xx.xx/ 2006/145. [25] Xxxx-Xxxxx Xx¨ck. Algebraic A note on elliptic curves over finite fields. Math. Comp., 49(179):301–304, 1987. [26] Ren´e Xxxxxx. Nonsingular plane cubic curves over finite fields. J. Combin. Theory Ser. A, 46(2):183–211, 1987. [27] Xxxxx Xxxxxxxxxxx. R´edei-matrices and applications. In Number theory (Paris, 1992–1993), volume 215 of London Math. Soc. Lecture Note Ser., pages 245–259. Cambridge Univ. Press, Cambridge, 1995. [28] Xxxxx Xxxxxxxxx. Cryptographic schemes based on isogenies. 2012. PhD thesis. xxxxx://xxxxxxxx.xxxx.xx/ntnu-xmlui/bitstream/handle/11250/262577/ 529395_FULLTEXT01.pdf. [29] G´xxxxx Xxxxxxxxx. Introduction to analytic and probabilistic number theory, volume 110 163 of Graduate Texts Studies in Mathematics. Springer-VerlagAmerican Mathematical Society, New YorkProvidence, second edition, 1994. [22] Xxxxx Xxxx. Algebra, volume 211 of Graduate Texts in Mathematics. Springer-Verlag, New YorkRI, third edition, 20022015. [23] St´ephane Louboutin. On Translated from the class number one problem for nonnor- mal quartic CM-fields. Tohoku Math. J. (2), 46(1):1–12, 1994. [24] St´ephane Louboutin. CM-fields with cyclic ideal class groups of 2-power orders. J. Number Theory, 67(1):1–10, 1997. [25] St´ephane Louboutin. Explicit upper bounds for residues of Dedekind zeta functions and values of L-functions at s = 1, and explicit lower bounds for relative class numbers of CM-fields. Canad. J. Math2008 French edition by Xxxxxxx X. X. Xxx., 53(6):1194–1222, 2001. [26] St´ephane Louboutin. Explicit lower bounds for residues at s = 1 of Dedekind zeta functions and relative class numbers of CM-fields. Trans. Amer. Math. Soc., 355(8):3079–3098, 2003. [27] St´xxxxxx Xxxxxxxxx, Xxxxxxx Xxxxxxx, and Xxxxxx Xxxxxxx. The class number one problem for some non-abelian normal CM-fields. Trans. Amer. Math. Soc., 349(9):3657–3678, 1997.

Bibliography. [1] Xxxx Xxxxxxxx, Xxxxxxxx Xxxxxxxxx, and Xxxxxxxx Xxxxxxxxxxx. CSI-FiSh: Ef- ficient isogeny based signatures through class group computations. In Asia- crypt (1), volume 11921 of Lecture Notes in Computer Science, pages 227–247. Springer, 2019. xxxxx://xx.xx/2018/485. [2] Xxx Xxxxx, Xxxxxx Xxxxx, and Xxxxxxxxx Xxx. Oblivious pseudorandom func- tions from isogenies. In Asiacrypt (2), volume 12492 of Lecture Notes in Computer Science, pages 520–550. Springer, 2020. xxxxx://xx.xx/2020/1532. [3] Xxxx Xxxxx and Xxxxx Xxxxxxxxxxx. On the computation of quadratic 2-class groups. J. Th´eor. Nombres Bordeaux, 8(2):283–313, 1996. [4] Xxxxxx Xxxxxxxx and Xxxxxx Xxxxx. CSIDH on the surface. In Xxxxxx Xxxx and Xxxx-Xxxxxx Xxxxxxx, editors, PQCrypto 2020, volume 12100 of Lecture Notes in Computer Science, pages 111–129. Springer, 2020. [5] Xxxxxx Xxxxxxxx, Xxx Xxxxx, Xxxxx Xxxxxxxxx, and Xxxxxxxxx Xxxxxxx. A fusion algorithm for solving the hidden shift problem in finite abelian groups. In PQCrypto, volume 12841 of Lecture Notes in Computer Science, pages 133–153. Springer, 2021. xxxxx://xxxxxx.xxxx.xxx/2021/562. [6] Xxxxxx Xxxxxxxx, Xxxxx Xxxxx, Xxxxx Xxxxxxxxxx, Xxxxxx Xxxxx, and Xxxxx Xxxxx. CSIDH: An efficient post-quantum commutative group action. In Asia- crypt 2018 Pt. 3, volume 11274 of Lecture Notes in Computer Science, pages 395–427. Springer, 2018. [7] Xxxxxx Xxxxxxxx, Xxxxxx Xxxxx, and Xxxxxxxx Xxxxxxxxxxx. Rational isogenies from irrational endomorphisms. In Eurocrypt (2), volume 12106 of Lecture Notes in Computer Science, pages 523–548. Springer, 2020. xxxxx://xx.xx/2019/1202. [8] Xxxxxx Xxxxxxxx, Xxxx Xxx´xxxx´a, and Xxxxxxxx Xxxxxxxxxxx. Breaking the de- cisional Xxxxxx-Xxxxxxx problem for class group actions using genus theory. In Crypto (2), volume 12171 of Lectures Notes in Computer Science, pages 92–120. Springer, 2020. xxxxx://xx.xx/2020/151. [9] Xxxxxxx Xxxxxx Xxxxxxxx Xxxxx and Xxxxx XxxxxxXxxxxxxx Xxxxx. Examples of CM curves of genus two defined over the reflex fieldHigher-degree supersingular group actions. LMS J. ComputIn MathCrypt, X. Math. Math.Cryptol. (to appear), 18(1):507– 538, 20152021. xxxxx://xx.xx/2021/955. [10] Xxxxxxxx Xxx`o and Xxxxx Xxxxx. Advanced topics in computational number theoryOrienting supersingular isogeny graphs. Journal of Mathematical Cryptolology, vol- ume 193 of Graduate Texts in Mathematics. Springer-Verlag14(1):414–437, New York, 20002020. [11] Xxxx-Xxxx Xxxxxxxxxx. Hard homogeneous spaces, 2006. Unpublished article, available at xxxxx://xxxxxx.xxxx.xxx/2006/291. [12] Xxxxx X. Xxx. Primes of the form x2 ++ ny2. Pure and Applied Math- ematics (Hoboken). Xxxx Xxxxx & Sons, Inc., Hoboken, NJ, second edition, 2013. Xxxxxx: Fermat, class field theory, and complex multiplication. [12] Xxxxx XxxxxxPure and Applied Mathematics. The structure of Galois groups of CM-fields. Trans. Amer. Math. Soc.Wiley, 283(1):1–32second edition, 19842013. [13] Xxxxx Xxxxx et alXxxxxxxx Xxxxxxx and Xxxx Xx Xxx. Echidna algorithms for algebra and geometry experimentationOn the security of OSIDH. xxxx://xxxxxxx.xxxxx.xxxx.xxx.xx/˜xxxxx/ dbs/complex_multiplication2.htmlIn PKC (1), volume 13177 of Lecture Notes in Computer Science, pages 52–81. Springer, 2022. xxxxx://xx.xx/2021/1681. [14] Xxxx X. Xx Xxx, Cyprien Delpech de Saint Guilhem, Xxxx Xxxxx Xxxxxxx, P´eter Xx- xxx, Xxxxxxx Xxxxxx, Xxxxxxxxxx Xxxxx, Xxxxxx Xxxxx, and Xxxxxxx X. XxxxxxXxxxxxxx Xxxxxxxxxx. Genus 2 curves with complex multiplicationS´eta: Supersingular encryption from torsion attacks. IntIn Asiacrypt (4), volume 13093 of Lecture Notes in Computer Science, pages 249–278. MathSpringer, 2021. Res. Not. IMRN, (5):1068–1142, 2012xxxxx://xx.xx/2019/1291. [15] Xxxxx XxxxxxxxxxXxxx Xx Xxx and Xxxxxxx Xxxxx. Algebraic geometryThreshold schemes from isogeny assumptions. In PKC (2), volume 12111 of Lecture Notes in Computer Science, pages 187–212. Springer-Verlag, New York- Heidelberg, 19772020. Graduate Texts in Mathematics, No. 52xxxxx://xx.xx/2019/1288. [16] Xxxx Xxxxx Xxxxxxx, P´eter Xxxxx, Xxxxx-Xxxxxxx Merz, and Xxx Xx Xx. Diophantische Analysis und ModulfunktionenOn the isogeny problem with torsion point information. MathIn PKC (1), volume 13177 of Lecture Notes in Computer Science, pages 142–161. Z.Springer, 56:227–253, 19522022. https: //xx.xx/0000/000. [17] Pınar Kılı¸cerXxxxxx X. Xxxxxxxxx, Xxxxxxxxxx Xxxxx, Xxxxx Xxxxx, and Xxx Xx Xx. Sage packages for computing On the security of supersingular isogeny cryptosystems. In Asiacrypt (non-biquadratic) quartic fields with CM class number one1), volume 10031 of Lecture Notes in Computer Science, pages 63–91. xxxx://xxx.xxxxSpringer, 2016. xxxxxxxxxx.xx/˜kilicerp/codes/, 2015https:// xx.xx/0000/000. [18] Pınar Kılı¸cer Xxxxx Xxx and Xxxxx XxxxxxXxxx Xx Xxx. The CM class number one problem for curves Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. In PQCrypto, volume 7071 of genus 2Lecture Notes in Computer Science, pages 19–34. xxxx://xxxxx.xxx/pdf/1511.04869v1.pdfSpringer, 20152011. xxxxx://xx.xx/2011/506. [19] Xxxxx Xxxxx X. Xxxxxxx and Xxxxxxxx XxxxXxxxxxxxxxx Xxxxx. Construction of XX Xxxxxx curvesFast polynomial factorization and modular composition. In IEEE FOCS 2008, pages 146–155, 2008. xxxx://xxxxx. xxx.xxxxxxx.xxx/~xxxxx/xxxxxx/XX00-xxxxx.xxx. [20] Xxxxx XxxxYi-Fu Xxx, Xxxxxx X. Xxxxxxxxx, and Xxxxxxx Xxxxxxx de Saint Guilhem. Complex multiplicationCom- pact, efficient and UC-secure isogeny-based oblivious transfer. In Eurocrypt (1), volume 255 12696 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Math- ematical Sciences]Lecture Notes in Computer Science, pages 213–241. Springer-Verlag, New York, 19832021. xxxxx://xx.xx/2020/1012. [21] Xxxxx X. Xxxxx. Complex multiplication (v0.10), 2020. xxxxx://xxx.xxxxxx. org/math/CourseNotes/cm.html. [22] Xxxxxxx Xxxxx. On oriented supersingular elliptic curves. Finite Fields Appl., 69:Paper No. 101777, 18, 2021. [23] Xxxxxxx Xxxxx. Probabilistic algorithms in finite fields. SIAM J. Com- put., 9(2):273–280, 1980. xxxx://xxxxxxxxxxxx.xxxxx.xxx.xxx/lcs/pubs/ pdf/MIT-LCS-TR-213.pdf. [24] Xxxxxxxxx Xxxxxxxxxx and Xxxxx Xxxxxxxxx. Public-key cryptosystem based on isogenies. IACR Cryptology ePrint Archive 2006/145, 2006. xxxxx://xx.xx/ 2006/145. [25] Xxxx-Xxxxx Xx¨ck. Algebraic A note on elliptic curves over finite fields. Math. Comp., 49(179):301–304, 1987. [26] Ren´e Xxxxxx. Nonsingular plane cubic curves over finite fields. J. Combin. Theory Ser. A, 46(2):183–211, 1987. [27] Xxxxx Xxxxxxxxxxx. R´edei-matrices and applications. In Number theory (Paris, 1992–1993), volume 215 of London Math. Soc. Lecture Note Ser., pages 245–259. Cambridge Univ. Press, Cambridge, 1995. [28] Xxxxx Xxxxxxxxx. Cryptographic schemes based on isogenies. 2012. PhD thesis. xxxxx://xxxxxxxx.xxxx.xx/ntnu-xmlui/bitstream/handle/11250/262577/ 529395_FULLTEXT01.pdf. [29] G´xxxxx Xxxxxxxxx. Introduction to analytic and probabilistic number theory, volume 110 163 of Graduate Texts Studies in Mathematics. Springer-VerlagAmerican Mathematical Society, New YorkProvidence, second edition, 1994. [22] Xxxxx Xxxx. Algebra, volume 211 of Graduate Texts in Mathematics. Springer-Verlag, New YorkRI, third edition, 20022015. [23] St´ephane Louboutin. On Translated from the class number one problem for nonnor- mal quartic CM-fields. Tohoku Math. J. (2), 46(1):1–12, 1994. [24] St´ephane Louboutin. CM-fields with cyclic ideal class groups of 2-power orders. J. Number Theory, 67(1):1–10, 1997. [25] St´ephane Louboutin. Explicit upper bounds for residues of Dedekind zeta functions and values of L-functions at s = 1, and explicit lower bounds for relative class numbers of CM-fields. Canad. J. Math2008 French edition by Xxxxxxx X. X. Xxx., 53(6):1194–1222, 2001. [26] St´ephane Louboutin. Explicit lower bounds for residues at s = 1 of Dedekind zeta functions and relative class numbers of CM-fields. Trans. Amer. Math. Soc., 355(8):3079–3098, 2003. [27] St´xxxxxx Xxxxxxxxx, Xxxxxxx Xxxxxxx, and Xxxxxx Xxxxxxx. The class number one problem for some non-abelian normal CM-fields. Trans. Amer. Math. Soc., 349(9):3657–3678, 1997.

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Echidna algorithms for algebra and geometry experimentation. xxxx://xxxxxxx.xxxxx.xxxx.xxx.xx/˜xxxxx/ dbs/complex_multiplication2.html. [14] Xxxx X. Xxxxx and Revised by Xxxxxxx X. Xxxxxx. Genus 2 curves Xxxxxxxxxx, Xxxxxxxxx Xxxxxxxx and X. X. Xxxxxxxxxxxx and with complex multiplication. Int. Math. Res. Not. IMRN, (5):1068–1142, 2012. [15] Xxxxx a preface by Xxxxxxxxxx. Algebraic geometry. Springer-Verlag, New York- Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. [16] Xxxx Xxxxxxx. Diophantische Analysis und Modulfunktionen. Math. Z., 56:227–253, 1952. [17] Pınar Kılı¸cer. Sage packages for computing (non-biquadratic) quartic fields with CM class number one. xxxx://xxx.xxxx. xxxxxxxxxx.xx/˜kilicerp/codes/, 2015. [18] Pınar Kılı¸cer and Xxxxx Xxxxxx. The CM class number one problem for curves of genus 2. xxxx://xxxxx.xxx/pdf/1511.04869v1.pdf, 2015. [19] Xxxxx Xxxxx and Xxxxxxxx Xxxx. Construction of XX Xxxxxx curves. [20] Xxxxx Xxxx. Complex multiplication, volume 255 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Math- ematical Sciences]. Springer-Verlag, New York, 1983. [21] Xxxxx Xxxx. Algebraic number theory, volume 110 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1994. [22] Xxxxx Xxxx. Algebra, volume 211 of Graduate Texts in Mathematics. Springer-Verlag, New York, third edition, 2002. [23] St´ephane Louboutin. On the class number one problem for nonnor- mal quartic CM-fields. Tohoku Math. J. (2), 46(1):1–12, 1994. [24] St´ephane Louboutin. CM-fields with cyclic ideal class groups of 2-power orders. J. Number Theory, 67(1):1–10, 1997. [25] St´ephane Louboutin. Explicit upper bounds for residues of Dedekind zeta functions and values of L-functions at s = 1, and explicit lower bounds for relative class numbers of CM-fields. Canad. J. Math., 53(6):1194–1222, 2001. [26] St´ephane Louboutin. Explicit lower bounds for residues at s = 1 of Dedekind zeta functions and relative class numbers of CM-fields. Trans. Amer. Math. Soc., 355(8):3079–3098, 2003. [27] St´xxxxxx Xxxxxxxxx, Xxxxxxx Xxxxxxx, and Xxxxxx Xxxxxxx. The class number one problem for some non-abelian normal CM-fields. Trans. Amer. Math. Soc., 349(9):3657–3678, 1997.