FAST COMPUTATION OF HALF-INTEGRAL WEIGHT MODULAR FORMS

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İNAM İ., Wiese G.

Rocky Mountain Journal of Mathematics, vol.52, no.4, pp.1395-1401, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.1216/rmj.2022.52.1395
  • Journal Name: Rocky Mountain Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1395-1401
  • Keywords: computation, Fourier coefficients, modular forms of half-integral weight, Rankin-Cohen operators
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© Rocky Mountain Mathematics Consortium.To study statistical properties of modular forms, including for instance Sato-Tate like problems, it is essential to be able to compute a large number of Fourier coefficients. We show that this can be achieved in level 4 for a large range of half-integral weights by making use of one of three explicit bases, the elements of which can be calculated via fast power series operations.