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Sign changes of Fourier coefficients for holomorphic eta-quotients

Kathrin Bringmann, Guoniu Han, Bernhard Heim, Ben Kane

Abstract

In this paper we study sign changes of an infinite class of $η$-quotients which are holomorphic modular forms. There is also a relation to Hurwitz class numbers.

Sign changes of Fourier coefficients for holomorphic eta-quotients

Abstract

In this paper we study sign changes of an infinite class of -quotients which are holomorphic modular forms. There is also a relation to Hurwitz class numbers.

Paper Structure

This paper contains 22 sections, 25 theorems, 116 equations.

Table of Contents

  1. Introduction and statement of results
  2. Preliminaries
  3. Modular forms
  4. Operators on (non-holomorphic) modular forms
  5. Eisenstein series
  6. Hecke operators
  7. Valence formula
  8. $L$-functions of Dirichlet characters
  9. Hurwitz class numbers
  10. Proof of Theorem \ref{['thm:M=1']}
  11. Proof of Theorem \ref{['thm:132-233']}
  12. Proof of Theorem \ref{['thm:14243-2']}
  13. Decomposition of the eta-quotient
  14. Fourier coefficients of the Eisenstein series part
  15. Finishing the proof of Theorem \ref{['thm:14243-2']}
  16. ...and 7 more sections

Key Result

Theorem 1.1

For $n\in\mathbb N_0$, we have

Theorems & Definitions (39)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Theorem 1.5
  • Corollary 1.6
  • Theorem 1.7
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • ...and 29 more