On the integral of the fourth Jacobi theta function

Details On the integral of the fourth Jacobi theta function On the integral of the fourth Jacobi theta function

2011-06-06

arxiv.org/abs/1106.1042v1

Mathematics

Number Theory

Submitted to Journal of Number Theory

Scientific paper

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.

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