منابع مشابه
Modern Theory of Automorphic Forms ∗
The modern theory of automorphic forms is a response to many different impulses and influences, above all the work of Hecke, but also class-field theory and the study of quadratic forms, the theory of representations of reductive groups, and of complexmultiplication, but so far many of the most powerful techniques are the issue, direct or indirect, of the introduction by Maass and then Selberg ...
متن کاملProblems in the Theory of Automorphic Forms
1. There has recently been much interest, if not a tremendous amount of progress, in the arithmetic theory of automorphic forms. In this lecture I would like to present the views not of a number theorist but of a student of group representations on those of its problems that he finds most fascinating. To be more precise, I want to formulate a series of questions which the reader may, if he like...
متن کاملApplications of Spectral Theory of Automorphic Forms
on Γ\H, parametrized as λw = w(w−1). Haas listed the w-values. Haas thought he was solving the differential equation (∆ − λ)u = 0. Stark and Hejhal observed zeros of ζ and of an L-function on Haas’ list. This suggested an approach to proving the Riemann Hypothesis, since it seemed that zeros w of ζ might give eigenvalues λ = w(w − 1) of ∆. Since ∆ is a self-adjoint, nonpositive operator, these ...
متن کاملDirichlet series from automorphic forms
This integral trick assumes greater significance when the function f is known to have strong decay properties both at 0 and at ∞, since then the Mellin transform is entire in s. One way to ensure such rapid decay is via eigenfunction properties in the context of automorphic forms. [2] • The archetype Mellin transform: zeta from theta • Abstracting to holomorphic modular forms • Variation: wavef...
متن کاملAutomorphic Forms
We apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type U(1, n−1). These cohomology theories of topological automorphic forms (TAF ) are related to Shimura varieties in the same way that TMF is related to the moduli space of elliptic curves. We study the cohomology operations on these theories, and relate them to certain Hecke algebras. We c...
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2010
ISSN: 1029-8479
DOI: 10.1007/jhep05(2010)098