On the Zeros on the Critical Line of $L$-Functions Corresponding to Automorphic Cusp Forms

I. S. Rezvyakova

Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 456-475.

Résumé

We consider an automorphic cusp form of integer weight $k\ge1$, 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 lies on the critical line.

Détail

Keywords: automorphic cusp form, Riemann zeta function, Riemann hypothesis, Hecke operator, $L$-function, Jutila's circle method.

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