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An introduction to zeta functions. (English) Zbl 0790.11061
Waldschmidt, Michel (ed.) et al., From number theory to physics. Lectures of a meeting on number theory and physics held at the Centre de Physique, Les Houches (France), March 7-16, 1989. Berlin: Springer-Verlag. 1-63 (1992).
As the title says, this article is an introduction to zeta-functions. It is devoted mainly to the Riemann zeta-function and the Dedekind zeta- function for the Gaussian integers. The main topics covered are the analytic continuation and functional equation, the latter treatment covering Fourier transforms, the Poisson summation formula, theta functions and Mellin transforms. Numerous exercises are included. Overall this would make good easy reading for a beginning graduate student.
For the entire collection see [Zbl 0784.00021].

MSC:
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11M41 Other Dirichlet series and zeta functions
11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
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