Nonvanishing of central L-values of Maass forms
نویسندگان
چکیده
منابع مشابه
Integral Traces of Singular Values of Weak Maass Forms
We define traces associated to a weakly holomorphic modular form f of arbitrary negative even integral weight and show that these traces appear as coefficients of certain weakly holomorphic forms of half-integral weight. If the coefficients of f are integral, then these traces are integral as well. We obtain a negative weight analogue of the classical Shintani lift and give an application to a ...
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The purpose of this paper is to give a generalization of the above result to the case of a Siegel cusp form f , where now L(f, χ, s) is replaced by an appropriate χ-twist of the Koecher-Maass series attached to f . More precisely, let f be a cusp form of even integral weight k ≥ g + 1 w.r.t. the Siegel modular group Γg := Spg(Z) of genus g and write a(T ) (T a positive definite half-integral ma...
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Let D ≡ 7 mod 8 be a positive squarefree integer, and let hD be the ideal class number of ED = Q( √−D). Let d ≡ 1 mod 4 be a squarefree integer relatively prime to D. Then for any integer k ≥ 0 there is a constant M = M(k), independent of the pair (D, d), such that if (−1)k = sign(d), (2k + 1, hD) = 1, and √ D > 12 π d(log |d|+ M(k)), then the central L-value L(k + 1, χ D,d ) > 0. Furthermore, ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2018.05.017