Displaying similar documents to “Automorphic L -functions in the weight aspect.”

A local large sieve inequality for cusp forms

Jonathan Wing Chung Lam (2014)

Journal de Théorie des Nombres de Bordeaux

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We prove a large sieve type inequality for Maass forms and holomorphic cusp forms with level greater or equal to one and of integral or half-integral weight in short interval.

Eisenstein series and Poincaré series for mixed automorphic forms.

Min Ho Lee (2000)

Collectanea Mathematica

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Mixed automorphic forms generalize elliptic modular forms, and they occur naturally as holomorphic forms of the highest degree on families of abelian varieties parametrized by a Riemann surface. We construct generalized Eisenstein series and Poincaré series, and prove that they are mixed automorphic forms.

From pseudodifferential analysis to modular form theory

André Unterberger (1999)

Journées équations aux dérivées partielles

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Taking advantage of methods originating with quantization theory, we try to get some better hold - if not an actual construction - of Maass (non-holomorphic) cusp-forms. We work backwards, from the rather simple results to the mostly devious road used to prove them.

Real zeros of holomorphic Hecke cusp forms

Amit Ghosh, Peter Sarnak (2012)

Journal of the European Mathematical Society

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This note is concerned with the zeros of holomorphic Hecke cusp forms of large weight on the modular surface. The zeros of such forms are symmetric about three geodesic segments and we call those zeros that lie on these segments, real. Our main results give estimates for the number of real zeros as the weight goes to infinity.

Nonvanishing of automorphic L-functions at special points

Zhao Xu (2014)

Acta Arithmetica

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At some special points, we establish a nonvanishing result for automorphic L-functions associated to the even Maass cusp forms in short intervals by using the mollification technique.