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Transactions of the American Mathematical Society

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Modular forms of weight $\frac 12$ 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
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Abstract: We continue Starkโ€™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.

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  • Erich Hecke, Lectures on the theory of algebraic numbers, Graduate Texts in Mathematics, vol. 77, Springer-Verlag, New York-Berlin, 1981. Translated from the German by George U. Brauer, Jay R. Goldman and R. Kotzen. MR 638719
  • Serge Lang, Algebraic number theory, 2nd ed., Graduate Texts in Mathematics, vol. 110, Springer-Verlag, New York, 1994. MR 1282723
  • J. Rhodes, Modular forms on $p$-adic upper half-planes, Ph.D. thesis, M.I.T., 1986.
  • 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. 27โ€“67. Lecture Notes in Math., Vol. 627. MR 0472707
  • Goro Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440โ€“481. MR 332663, DOI
  • 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. 421โ€“455. MR 894333
  • ---, Lecture at the 4th Annual Workshop on Automorphic Forms and Related Topics, Hanover, N.H., December 1989.
  • Audrey Terras, Harmonic analysis on symmetric spaces and applications. I, Springer-Verlag, New York, 1985. MR 791406
  • A. Weil, Dirichlet series and automorphic forms, Lecture Notes in Math., vol. 189, Springer-Verlag, New York, 1971.

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Article copyright: © Copyright 1993 American Mathematical Society