Displaying similar documents to “Siegel Cusp Forms as Holomorphic Differential Forms on Certain Compact Varieties.”

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.

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.

Shimura lifting on weak Maass forms

Youngju Choie, Subong Lim (2016)

Acta Arithmetica

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There is a Shimura lifting which sends cusp forms of a half-integral weight to holomorphic modular forms of an even integral weight. Niwa and Cipra studied this lifting using the theta series attached to an indefinite quadratic form; later, Borcherds and Bruinier extended this lifting to weakly holomorphic modular forms and harmonic weak Maass forms of weight 1/2, respectively. We apply Niwa's theta kernel to weak Maass forms by using a regularized integral. We show that the lifted function...