On the integral of the fourth Jacobi theta function

István Mező

On the integral of the fourth Jacobi theta function

Number Theory 2011-06-07 v1

Authors: István Mező

Abstract

We generalize the Raabe-formula to the $q$ -loggamma function. As a consequence, we get that the integral of the logarithm of the fourth Jacobi theta function between its least imaginary zeros is connected to the partition function and the Riemann zeta function.

Keywords

zeta functions riemann zeta function jacobi forms

Cite

@article{arxiv.1106.1042,
  title  = {On the integral of the fourth Jacobi theta function},
  author = {István Mező},
  journal= {arXiv preprint arXiv:1106.1042},
  year   = {2011}
}

Comments

Submitted to Journal of Number Theory

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