Abstract
The functional equation for Dirichlet’s L functions was first given by Hurwitz in 1882 (Werke I, pp. 72–88), though he confined himself to real characters since he was primarily interested in L functions in relation to quadratic forms. He first obtained the functional equation for the more general ζ function ζ(s, w), which will be given below, and deduced that of the L functions from it. We shall follow the method used by de la Vallée Poussin in 1896, which is an extension of that of Riemann used in the preceding section.
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References
See, for example, Titchmarsh, §2.17.
J. London Math. Soc., 11, 181–185 (1936).
J. London Math. Soc., 36, 177–184 (1961).
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© 1980 Ann Davenport
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Davenport, H. (1980). The Functional Equation of the L Functions. In: Multiplicative Number Theory. Graduate Texts in Mathematics, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5927-3_9
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DOI: https://doi.org/10.1007/978-1-4757-5927-3_9
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