• Corpus ID: 56182619

The Stokes phenomenon and the Lerch zeta function

@article{Paris2016TheSP,
  title={The Stokes phenomenon and the Lerch zeta function},
  author={Richard B. Paris},
  journal={arXiv: Classical Analysis and ODEs},
  year={2016}
}

• R. Paris
• Published 30 January 2016
• Mathematics
• arXiv: Classical Analysis and ODEs

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.