Titlebook: Automorphic Forms, Representation Theory and Arithmetic; Papers presented at Gelbart Harder Iwasawa,Jacquet Katz Piatetski-Shap Conference

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https://doi.org/10.1007/978-1-4899-6683-4G. Shimura has shown how to attach to each holomorphic cusp form of half-integral weight a modular form of even integral weight. More precisely, suppose f(z) is a cusp form of weight k/2, level N, and character χ.

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The Transport of Acid PollutionOur starting point is a very general question. Let Γ be an arithmetic subgroup of a reductive Lie group G.. Then the group T acts on the symmetric space X = G./K. where K. ? G. is a maximal compact subgroup.

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Strategies for Reducing Acid RainSuppose . is a modular cusp form with Fourier expansion:

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,On Shimura’s Correspondence for Modular Forms of Half-Integral Weight,G. Shimura has shown how to attach to each holomorphic cusp form of half-integral weight a modular form of even integral weight. More precisely, suppose f(z) is a cusp form of weight k/2, level N, and character χ.

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,On P-ADIC Representations Associated with ?p -Extensions,. paper, we shall discuss some results on the p-adic representations of Galois groups, associated with so-called cyclotomic ?.-extensions of finite algebraic number fields.

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Dirichlet Series for the Group GL(N),Suppose . is a modular cusp form with Fourier expansion: