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On real quadratic fields
Author(s):
Gilles
Lachaud
Journal:
Bull. Amer. Math. Soc.
17
(1987),
307-311.
MSC (1985):
Primary 11E45, 11M41, 11R29, 11R42;
Secondary 11E32, 11E41, 11M20, 11R11
MathSciNet review:
903739
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References:
- F. Çallialp, Non-nullité des fonctions zêta des corps quadratiques réels pour 0 < s < 1, C. R. Acad. Sci. Paris 291 (1980), 623-625. MR 606448
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- D. Goldfeld and A. Schinzel, On Siegel's zero, Ann. Sci. Norm. Sup. Pisa IV 2 (1975), 571-585. MR 404213
- D. Goldfeld, The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer, Ann. Sci. Norm. Sup. Pisa IV 3 (1976), 623-663. MR 450233
- E. Hecke, Über die Kroneckersche grenzformel für reelle quadratische körper und die classenzahl relativ-abelscher körper, Mathematische Werke, Vandenhoeck und Ruprecht, Göttingen, 1970; no. 10, 1917. MR 371577
- S. Lang, Algebraic number theory, Addison-Wesley, Reading, 1970. MR 282947
- Casimir Richaud, Sur la résolution des équations x2 - Ay2 = ±1, Atti dell'Acc. Pont, de Nuovi Lincei (1866), 177-182.
- T. Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, J. Fac. Sci. Univ. Tokyo, Sect. IA 23 (1976), 393-417. MR 427231
- C. L. Siegel, Über die Classenzahl quadratischer Zahlkörper, Acta Arith. 1 (1935), 83-86; =Ges. Abh., no. 21, I, pp. 406-409, Springer, Berlin, 1966.
- H. Stark, On the problem of unique factorization in complex quadratic fields, Proc. Sympos. Pure Math., vol. 12, Amer. Math. Soc. Providence, R.I., 1969, pp. 41-56. MR 252350
- T. Vijayaraghavan, Periodic simple continued fractions, Proc. London Math. Soc. 26 (1927), 403-414.
- F. Wielonsky, Séries d'Eisenstein, intégrales toroïdales et une formule de Hecke, Enseign. Math. 31 (1985), 93-135. MR 798908
- D. Zagier, A Kronecker limit formula for real quadratic fields, Math. Ann. 213 (1975), 153-184. MR 366877
- D. Zagier, Valeurs des fonctions zêta des corps quadratiques réels aux entiers négatifs, J. Arith. Caen, Astérisque 41-42 (1977), 135-151. MR 441925
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11E45, 11M41, 11R29, 11R42, 11E32, 11E41, 11M20, 11R11
Additional Information:
DOI:
10.1090/S0273-0979-1987-15571-6
PII:
S 0273-0979(1987)15571-6
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