Titlebook: Non-vanishing of L-Functions and Applications; M. Ram Murty,V. Kumar Murty Book 1997 Springer Basel AG 1997 Number theory.alegbraic geomet

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Non-Vanishing of Quadratic Twists of Modular ,-Functions,Let . be a holomorphic cusp form for Γ.(.) of weight 2 and character ∈. We assume that . is a normalized newform for the Hecke operators. Denote by .(.) the .-function attached to . For Re(.) > 3/2, it is given by an absolutely convergent Dirichlet seriesLleft( {s,f} ight) = sumlimits_{{n = 1}}^{infty } {frac{{aleft( n ight)}}{{{n^{s}}}}} .

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,Selberg’s Conjectures,In a fundamental paper [S], Selberg defined a general class of Dirichlet series and formulated basic conjectures concerning them. Selberg’s conjectures concern Dirichlet series, which admit analytic continuations, Euler products and functional equations.

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M. Ram Murty,V. Kumar Murtyormance using the new method. Material is included which shows how the new technique can be extended to the control of a broad range of large-scale complex nonlinear processes..978-1-4471-2615-7978-0-85729-067-0Series ISSN 1430-9491 Series E-ISSN 2193-1577