publication . Article . Preprint . 2017

The multiple Dirichlet product and the multiple Dirichlet series

Tomokazu Onozuka;
Open Access
  • Published: 02 Aug 2017 Journal: International Journal of Number Theory, volume 13, pages 2,181-2,193 (issn: 1793-0421, eissn: 1793-7310, Copyright policy)
  • Publisher: World Scientific Pub Co Pte Lt
Abstract
Comment: 15 pages
Subjects
arXiv: Mathematics::Spectral TheoryMathematics::Analysis of PDEs
free text keywords: Algebra and Number Theory, Mathematics - Number Theory, 11M32, 11A25, Pure mathematics, Reciprocal, Multiple zeta function, Dirichlet series, symbols.namesake, symbols, Mathematics, Dirichlet distribution
Related Organizations

[1] S. Akiyama, S. Egami and Y. Tanigawa, Analytic continuation of multiple zeta-functions and their values at non-positive integers, Acta Arith, 98 (2001), 107-116. [OpenAIRE]

[2] S. Akiyama and H. Ishikawa, On analytic continuation of multiple Lfunctions, Analytic Number Theory, C. Jia and K. Matsumoto, eds. (2002), 1-16.

[3] E. D. Cashwell and C. J. Everett, The ring of number-theoretic functions, Pacific J. Math. 9 (1959), 975-985. [OpenAIRE]

[4] R. de la Bret´eche, Estimation de sommes multiples de fonctions arith´etiques, Compositio Mathematica 128 (2001), 261-298.

[5] M. Hoffman, Multiple harmonic series, Pacific J. Math., 152 (1992), 275-290.

[6] K. Matsumoto, On analytic continuation of various multiple zetafunctions, Number Theory for the Millenium (Urbana, 2000), Vol. II, M. A. Bennett et. al. (eds.), A. K. Peters, Natick, MA, 2002, pp. 417- 440.

[7] K. Matsumoto, On Mordell-Tornheim and other multiple zeta-functions, In: Proc. Session in Analytic Number Theory and Diophantine Equations, (eds. D. R. Heath-Brown and B. Z. Moroz), Bonner Math. Schriften, 360, Bonn, 2003, n.25, 17pp.

[8] K. Matsumoto and Y. Tanigawa, The analytic continuation and the order estimate of multiple Dirichlet series, J. Th´eorie des Nombres de Bordeaux, 15 (2003), 267-274.

[9] R. Spira, Zero-free regions of ζ(k)(s), J. London Math. Soc., 40 (1965), 677-682.

[10] L. T´oth, Multiplicative arithmetic functions of several variables: a survey, preprint, arXiv:1310.7053.

[11] J. Zhao, Analytic continuation of multiple zeta functions, Proc. Amer. Math. Soc. 128 (2000), 1275-1283.

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