• Corpus ID: 202149244

ASYMPTOTIC EXPANSIONS FOR THE LAPLACE-MELLIN AND RIEMANN-LIOUVILLE TRANSFORMS OF LERCH ZETA-FUNCTIONS : PRE-ANNOUNCEMENT VERSION (Analytic Number Theory and Related Areas)

@inproceedings{Katsurada2017ASYMPTOTICEF,
  title={ASYMPTOTIC EXPANSIONS FOR THE LAPLACE-MELLIN AND RIEMANN-LIOUVILLE TRANSFORMS OF LERCH ZETA-FUNCTIONS : PRE-ANNOUNCEMENT VERSION (Analytic Number Theory and Related Areas)},
  author={Masanori Katsurada},
  year={2017}
}
This article summarizes the results appearing in the forthcoming paper [13]. For a complex variable s , and real parameters a and $\lambda$ with a>0 , the Lerch zeta‐ function $\phi$(s, a, $\lambda$) is defined by the Dirichlet series \displaystyle \sum_{l=0}^{\infty}e( $\lambda$ l)(a+l)^{-s}({\rm Re} s>1) , and its meromorphic continuation over the whole s‐plane, where e( $\lambda$)=e^{2 $\pi$ i $\lambda$} , and the domain of the parameter a can be extended to the whole sector |\mathrm{a}x… 
1 Citations
Ja n 20 22 ASYMPTOTIC EXPANSIONS FOR THE LAPLACE-MELLIN AND RIEMANN-LIOUVILLE TRANSFORMS OF LERCH ZETA-FUNCTIONS
Abstract. Let φ(s, a, λ) denote the Lerch zeta-function, φ(s, a, λ) a slight modification of φ(s, a, λ) defined by extracting the (possible) singularity of φ(s, a, λ) at s = 1, and (φ)(s, a, λ) for

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