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

On the Ramanujan–Petersson conjecture for modular forms of half-integral weight AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

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

Gun, Sanoli; Kohnen, Winfried
Forum Mathematicum , Volume 31 (3): 9 – May 1, 2019
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Publisher
de Gruyter
Copyright
© 2019 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2018-0179
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Forum Mathematicum – de Gruyter

Published: May 1, 2019

References

  • Symmetric power L-functions for GL⁢(2){\rm GL}(2)
  • On modular forms of half integral weight
  • A family of Calabi–Yau varieties and potential automorphy II
  • Hecke operators in half-integral weight
  • On the coefficients of cusp forms
  • Twists of modular forms and endomorphisms of abelian varieties
  • Omega results for automorphic L-functions
  • Fourier coefficients of modular forms of half-integral weight