Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

On real quadratic fields


Author: 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
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • Fethi Çallialp, Non-nullité des fonctions zéta des corps quadratiques réels pour 0<𝑠<1, C. R. Acad. Sci. Paris Sér. A-B 291 (1980), no. 12, A623–A625 (French, with English summary). MR 606448 (82h:12014)
  • S. Chowla and J. B. Friedlander, Some remarks on 𝐿-functions and class numbers, Acta Arith. 28 (1975/76), no. 4, 413–417. MR 0389852 (52 #10682)
  • Atle Selberg and S. Chowla, On Epstein’s zeta-function, J. Reine Angew. Math. 227 (1967), 86–110. MR 0215797 (35 #6632)
  • E. P. Golubeva, The length of a period of quadratic irrationality, Mat. Sb. (N.S.) 123(165) (1984), no. 1, 120–129 (Russian). MR 728933 (85f:11044)
  • D. M. Goldfeld and A. Schinzel, On Siegel’s zero, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2 (1975), no. 4, 571–583. MR 0404213 (53 #8016)
  • Dorian M. Goldfeld, The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), no. 4, 624–663. MR 0450233 (56 #8529)
  • Erich Hecke, Mathematische Werke, Vandenhoeck\thinspace&\thinspace Ruprecht, Göttingen, 1970 (German). Mit einer Vorbemerkung von B. Schoenberg, einer Anmerkung von Carl Ludwig Siegel, und einer Todesanzeige von Jakob Nielsen; Zweite durchgesehene Auflage. MR 0371577 (51 #7795)
  • Serge Lang, Algebraic number theory, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0282947 (44 #181)
  • Casimir Richaud, Sur la résolution des équations x2 - Ay2 = ±1, Atti dell'Acc. Pont, de Nuovi Lincei (1866), 177-182.
  • Takuro Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), no. 2, 393–417. MR 0427231 (55 #266)
  • 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. M. Stark, On the problem of unique factorization in complex quadratic fields., Number Theory (Proc. Sympos. Pure Math, Vol. XII, Houston, Tex., 1967) Amer. Math. Soc., Providence, R.I., 1967, pp. 41–56. MR 0252350 (40 #5571)
  • T. Vijayaraghavan, Periodic simple continued fractions, Proc. London Math. Soc. 26 (1927), 403-414.
  • Franck Wielonsky, Séries d’Eisenstein, intégrales toroïdales et une formule de Hecke, Enseign. Math. (2) 31 (1985), no. 1-2, 93–135 (French). MR 798908 (87b:11042)
  • Don Zagier, A Kronecker limit formula for real quadratic fields, Math. Ann. 213 (1975), 153–184. MR 0366877 (51 #3123)
  • D. Zagier, Valeurs des fonctions zêta des corps quadratiques réels aux entiers négatifs, Journées Arithmétiques de Caen (Univ. Caen, Caen, 1976) Soc. Math. France, Paris, 1977, pp. 135–151. Astérisque No. 41–42 (French). MR 0441925 (56 #316)

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 11E45, 11M41, 11R29, 11R42, 11E32, 11E41, 11M20, 11R11

Retrieve articles in all journals with MSC (1985): 11E45, 11M41, 11R29, 11R42, 11E32, 11E41, 11M20, 11R11


Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1987-15571-6
PII: S 0273-0979(1987)15571-6