Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Modular forms of weight $ \frac12$ defined on products of $ p$-adic upper half-planes


Author: Anne Schwartz
Journal: Trans. Amer. Math. Soc. 335 (1993), 757-773
MSC: Primary 11F41; Secondary 11F37, 11F85
MathSciNet review: 1154543
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We continue Stark's study of modular forms defined on products of $ p$-adic upper half-planes. Specifically, we restrict to the case of the number field $ \mathbb{Q}$ and one finite prime. In this setting we develop a multiplier system for modular forms of weight $ \frac{1} {2}$, and provide an example of such a form.


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

  • [He] Erich Hecke, Lectures on the theory of algebraic numbers, Graduate Texts in Mathematics, vol. 77, Springer-Verlag, New York, 1981. Translated from the German by George U. Brauer, Jay R. Goldman and R. Kotzen. MR 638719 (83m:12001)
  • [La] Serge Lang, Algebraic number theory, 2nd ed., Graduate Texts in Mathematics, vol. 110, Springer-Verlag, New York, 1994. MR 1282723 (95f:11085)
  • [Rh] J. Rhodes, Modular forms on $ p$-adic upper half-planes, Ph.D. thesis, M.I.T., 1986.
  • [SS] J.-P. Serre and H. M. Stark, Modular forms of weight 1/2, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976), Springer, Berlin, 1977, pp. 27–67. Lecture Notes in Math., Vol. 627. MR 0472707 (57 #12400)
  • [Sh] Goro Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440–481. MR 0332663 (48 #10989)
  • [St1] H. M. Stark, Modular forms and related objects, Number theory (Montreal, Que., 1985) CMS Conf. Proc., vol. 7, Amer. Math. Soc., Providence, RI, 1987, pp. 421–455. MR 894333 (88j:11029)
  • [St2] -, Lecture at the 4th Annual Workshop on Automorphic Forms and Related Topics, Hanover, N.H., December 1989.
  • [Te] Audrey Terras, Harmonic analysis on symmetric spaces and applications. I, Springer-Verlag, New York, 1985. MR 791406 (87f:22010)
  • [We] A. Weil, Dirichlet series and automorphic forms, Lecture Notes in Math., vol. 189, Springer-Verlag, New York, 1971.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 11F41, 11F37, 11F85

Retrieve articles in all journals with MSC: 11F41, 11F37, 11F85


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1154543-7
PII: S 0002-9947(1993)1154543-7
Article copyright: © Copyright 1993 American Mathematical Society