Abstract
Since the time of Dirichlet and Riemann, the analytic properties of L-functions have been used to establish theorems of a purely arithmetic nature. The distribution of prime numbers in arithmetic progressions is intimately connected with non-vanishing properties of various L-functions. With the subsequent advent of the Tauberian theory as developed by Wiener and Ikehara, these arithmetical theorems have been shown to be equivalent to the non-vanishing of these L-functions on the line Re(s) = 1.
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© 1997 Springer Basel AG
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Murty, M.R., Murty, V.K. (1997). Introduction. In: Non-vanishing of L-Functions and Applications. Progress in Mathematics, vol 157. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8956-8_1
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DOI: https://doi.org/10.1007/978-3-0348-8956-8_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-5801-3
Online ISBN: 978-3-0348-8956-8
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