Analytic properties of multiple Dirichlet series associated to additive and Dirichlet characters View Full Text


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Article Info

DATE

2018-06-14

AUTHORS

Biswajyoti Saha

ABSTRACT

In this article, we study analytic properties of the multiple Dirichlet series associated to additive and Dirichlet characters. For the multiple Dirichlet series associated to additive characters, the meromorphic continuation is established via obtaining translation formulas satisfied by them. We then determine the exact set of singularities of such multiple Dirichlet series. While it seems difficult to obtain a similar translation formula for the multiple Dirichlet series associated to Dirichlet characters, we establish an intrinsic connection between them and the multiple Dirichlet series associated to additive characters. We rely on this connection to investigate the analytic characteristics of the multiple Dirichlet series associated to Dirichlet characters. More... »

PAGES

203-227

References to SciGraph publications

  • 2017-03-10. An elementary approach to the meromorphic continuation of some classical Dirichlet series in PROCEEDINGS - MATHEMATICAL SCIENCES
  • 2002. Multiple Polylogarithms: An Introduction in NUMBER THEORY AND DISCRETE MATHEMATICS
  • 2002. On Analytic Continuation of Multiple L-Functions and Related Zeta-Functions in ANALYTIC NUMBER THEORY
  • 2007-11-13. Analytic continuation of multiple polylogarithms in ANALYSIS MATHEMATICA
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    http://scigraph.springernature.com/pub.10.1007/s00229-018-1046-8

    DOI

    http://dx.doi.org/10.1007/s00229-018-1046-8

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