On the zeros on the critical line of L-functions corresponding to automorphic cusp forms

We consider an automorphic cusp form of integer weight k ≥ 1, which is the eigenfunction of all Hecke operators. It is proved that, for the L -series whose coefficients correspond to the Fourier coefficients of such an automorphic form, the positive fraction of nontrivial zeros lie on the critical l...

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Bibliographic Details
Published in:Mathematical Notes 2010-10, Vol.88 (3-4), p.423-439
Main Author: Rezvyakova, I. S.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We consider an automorphic cusp form of integer weight k ≥ 1, which is the eigenfunction of all Hecke operators. It is proved that, for the L -series whose coefficients correspond to the Fourier coefficients of such an automorphic form, the positive fraction of nontrivial zeros lie on the critical line.
ISSN:0001-4346
1573-8876
DOI:10.1134/S0001434610090154