On the Ramanujan–Petersson conjecture for modular forms of half-integral weight

Sanoli Gun; Winfried Kohnen

doi:10.1515/forum-2018-0179

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On the Ramanujan–Petersson conjecture for modular forms of half-integral weight

Sanoli Gun Winfried Kohnen

Year: 2019 Journal: Forum Mathematicum Vol: 31 (3)Pages: 703-711 Publisher: De Gruyter

DOI: 10.1515/forum-2018-0179

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Abstract

Abstract We investigate the (still unknown) Ramanujan–Petersson conjecture about the growth of the Fourier coefficients of cusp forms of half-integral weight and prove that it is optimal, at least for newforms in the plus space.

Keywords:

Mathematics Ramanujan's sum Conjecture Modular form Pure mathematics Modular design Combinatorics Computer science

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Advanced Algebra and Geometry

Physical Sciences → Mathematics → Mathematical Physics

Analytic Number Theory Research

Physical Sciences → Mathematics → Algebra and Number Theory

Advanced Mathematical Identities

Physical Sciences → Mathematics → Algebra and Number Theory

On the Ramanujan–Petersson conjecture for modular forms of half-integral weight

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