The asymptotic profile of an eta-theta quotient related to entanglement entropy in string theory

Abstract

In this paper we investigate a certain eta-theta quotient which appears in the partition function of entanglement entropy. Employing Wright's circle method, we give its bivariate asymptotic profile.Mathematics Subject Classification 2010: 11F50

Bivariate asymptotics for eta-theta quotients with simple poles

“…However, using the techniques presented here and shifting integrals to not have end-points at 0, 1 a similar story holds for functions without a theta function in the numerator. (3) For convenience with the use of the saddle-point method, we assume that b 2 = c. If this is not the case, a blend of techniques from the present paper and those in [8] would yield similar results.…”

“…Jacobi forms are ubiquitous throughout number theory and beyond. For example, they appear in string theory [8,11], the theory of black holes [5], and the combinatorics of partition statistics [3]. The Fourier coefficients of Jacobi forms often encode valuable arithmetic information.…”

“…Recently, the second author of the present paper extended these techniques to an example appearing in the partition function for entanglement entropy in string theory. In particular, [8] considered the eta-theta quotient ϑ(z; τ ) 4 η(τ ) 9 ϑ(2z; τ ) =:…”

“…(1) The exposition presented here may be easily generalised to include products of theta functions in both the numerator and denominator of f (thereby covering the case of [8]), although this becomes lengthy to write out for the general case.…”

Corrigendum to: The asymptotic profile of an eta-theta quotient related to entanglement entropy in string theory

“…This corrigendum deals with two issues in the article [1] kindly pointed out to the author by S. Zwegers. There is an error that occurs in the use of the integrals G + and G − , and another in the treatment of the functions g m,j for j = 1, 2, 3 where exponential growth should occur.…”