The Stokes phenomenon and the Lerch zeta function

Abstract

We examine the exponentially improved asymptotic expansion of the Lerch zeta function $L(\lambda ,a,s)={\sum }_{n=1}^{\infty }\exp (2\pi ni\lambda )/(n+a{)}^s$ for large complex values of $a$, with $\lambda$ and $s$ regarded as parameters. It is shown that an infinite number of subdominant exponential terms switch on across the Stokes lines $\arg a=\pm \pi /2$. In addition, it is found that the transition across the upper and lower imaginary $a$-axes is associated, in general, with unequal scales. Numerical calculations are presented to confirm the theoretical predictions.

13 pages, 0 figures. arXiv admin note: text overlap with arXiv:1407.2782

References in corpus (1)

• The Stokes phenomenon associated with the periodic zeta function $F(a,s)$