Analytic continuation and functional equation of L ( s , χ )
نویسنده
چکیده
Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/mfms/notes 2015-16/06d functional equation.pdf] 1. L(s, χ) for even χ 2. L(s, χ) for odd χ We prove the analytic continuation and function equation of Dirichlet L-functions L(s, χ) imitating the argument Riemann used for proving the analytic continuation of ζ(s) and its functional equation π−s/2 Γ( s 2 ) ζ(s) = π −(1−s)/2 Γ( 1−s 2 ) ζ(1− s) from the integral representation π−s/2 Γ( s 2 ) ζ(s) = ∫ ∞
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