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Nonvanishing and Central Critical Values...
Schwagenscheidt, Mar...

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Nonvanishing and Central Critical Values of Twisted $L$-functions of Cusp Forms on Average by Schwagenscheidt, Markus ( Author )
Lemonjar Open Access
N.A
09-02-2015
Let f be a holomorphic cusp form of integral weight k≥3 for Γ0(N) with nebentypus character ψ. Generalising work of Kohnen and Raghuram we construct a kernel function for the L-function L(f,χ,s) of f twisted by a primitive Dirichlet character χ and use it to show that the average ∑f∈Sk(N,ψ)L(f,χ,s)<f,f>af(1)¯ over an orthogonal basis of Sk(N,ψ) does not vanish on certain line segments inside the critical strip if the weight k or the level N is big enough. As another application of the kernel function we prove an averaged version of Waldspurger's theorem relating the central critical value of the D-th twist (D<0 a fundamental discriminant) of the L-function of a cusp form f of even weight 2k to the square of the |D|-th Fourier coefficient of a form of half-integral weight k+1/2 associated to f under the Shimura correspondence.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1502.02492
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