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Partition-Theoretic Results and Recurrence Relations for the Coefficients of Some Mock Theta Functions

Sabi Biswas, Nipen Saikia

Abstract

In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain restricted partition functions are also established.

Partition-Theoretic Results and Recurrence Relations for the Coefficients of Some Mock Theta Functions

Abstract

In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain restricted partition functions are also established.
Paper Structure (6 sections, 23 theorems, 116 equations)

This paper contains 6 sections, 23 theorems, 116 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Results on $v(q)$
  4. Results on $\sigma(q)$
  5. Results on $\beta(q)$
  6. Results on $\lambda(q)$

Key Result

Lemma 2.1

If p is an odd prime, then Furthermore, $\dfrac{m^{2}+m}{2} \not\equiv \dfrac{p^{2}-1}{8} \,(\textup{mod}\,p)\quad for\quad 0\leq m \leq \dfrac{p-3}{2}.$

Theorems & Definitions (43)

  • Lemma 2.1: CG
  • Lemma 2.2: CG
  • Lemma 2.3: AB
  • Lemma 2.4
  • Theorem 3.1
  • proof
  • Theorem 3.2
  • proof
  • Theorem 3.3
  • proof
  • ...and 33 more