منابع مشابه
Finite Analogs of Maass Wave Forms
Orthogonality relations for finite Eisenstein series are obtained. It is shown that there exist finite analogs of Maass wave forms which are not Eisenstein series.
متن کاملPeriod functions for Maass wave forms
Contents Introduction Chapter I. The period correspondence via L-series 1. The correspondences u ↔ Lε ↔ f ↔ ψ 2. Periodicity, L-series, and the three-term functional equation 3. Even and odd 4. Relations between Mellin transforms; proof of Theorem 1 Chapter II. The period correspondence via integral transforms 1. The integral representation of ψ in terms of u 2. The period function as the integ...
متن کاملRemarks on Modular Symbols for Maass Wave Forms
Abstract. In this paper I introduce modular symbols for Maass wave cusp forms. They appear in the guise of finitely additive functions on the Boolean algebra generated by intervals with non–positive rational ends, with values in analytic functions (pseudo–measures in the sense of [MaMar2]). After explaining the basic issues and analogies in the extended Introduction, I construct modular symbols...
متن کاملDeformations of Maass forms
We describe numerical calculations which examine the PhillipsSarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume Riemann surface S under deformation of the surface. Our calculations indicate that if the Teichmüller space of S is not trivial, then each cusp form has a set of deformations under which either the cusp form remains a cusp form or else it dissol...
متن کاملDyson’s Ranks and Maass Forms
which were defined by Ramanujan and Watson decades ago. In his last letter to Hardy dated January 1920 (see pages 127-131 of [27]), Ramanujan lists 17 such functions, and he gives 2 more in his “Lost Notebook” [27]. In his paper “The final problem: An account of the mock theta functions” [32], Watson defines 3 further functions. Surprisingly, much remains unknown about these enigmatic series. R...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2012-11557-6