Displaying similar documents to “On the products of Hecke L-functions of holomorphic cusp forms”

A local large sieve inequality for cusp forms

Jonathan Wing Chung Lam (2014)

Journal de Théorie des Nombres de Bordeaux

Similarity:

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.

On arbitrary products of eigenforms

Arvind Kumar, Jaban Meher (2016)

Acta Arithmetica

Similarity:

We characterize all the cases in which products of arbitrary numbers of nearly holomorphic eigenforms and products of arbitrary numbers of quasimodular eigenforms for the full modular group SL₂(ℤ) are again eigenforms.

Eisenstein series and Poincaré series for mixed automorphic forms.

Min Ho Lee (2000)

Collectanea Mathematica

Similarity:

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.

Real zeros of holomorphic Hecke cusp forms

Amit Ghosh, Peter Sarnak (2012)

Journal of the European Mathematical Society

Similarity:

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.

From pseudodifferential analysis to modular form theory

André Unterberger (1999)

Journées équations aux dérivées partielles

Similarity:

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.