Analytic and combinatoric aspects of Hurwitz polyzêtas

Jean-Yves Enjalbert[1]; Hoang Ngoc Minh[1]

  • [1] Université Lille II 1 place Déliot 59024 Lille, France

Journal de Théorie des Nombres de Bordeaux (2007)

  • Volume: 19, Issue: 3, page 595-640
  • ISSN: 1246-7405

Abstract

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In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to build the analytic continuation of Hurwitz polyzêtas as multivariate meromorphic functions.

How to cite

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Enjalbert, Jean-Yves, and Ngoc Minh, Hoang. "Analytic and combinatoric aspects of Hurwitz polyzêtas." Journal de Théorie des Nombres de Bordeaux 19.3 (2007): 595-640. <http://eudml.org/doc/249979>.

@article{Enjalbert2007,
abstract = {In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to build the analytic continuation of Hurwitz polyzêtas as multivariate meromorphic functions.},
affiliation = {Université Lille II 1 place Déliot 59024 Lille, France; Université Lille II 1 place Déliot 59024 Lille, France},
author = {Enjalbert, Jean-Yves, Ngoc Minh, Hoang},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {multiple Hurwitz zeta function; analytic continuation},
language = {eng},
number = {3},
pages = {595-640},
publisher = {Université Bordeaux 1},
title = {Analytic and combinatoric aspects of Hurwitz polyzêtas},
url = {http://eudml.org/doc/249979},
volume = {19},
year = {2007},
}

TY - JOUR
AU - Enjalbert, Jean-Yves
AU - Ngoc Minh, Hoang
TI - Analytic and combinatoric aspects of Hurwitz polyzêtas
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2007
PB - Université Bordeaux 1
VL - 19
IS - 3
SP - 595
EP - 640
AB - In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to build the analytic continuation of Hurwitz polyzêtas as multivariate meromorphic functions.
LA - eng
KW - multiple Hurwitz zeta function; analytic continuation
UR - http://eudml.org/doc/249979
ER -

References

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