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- W4299364458 abstract "In this paper we prove that the Generalized Riemann Hypothesis (GRH) for functions in the class $mathcal{S}^{sharpflat}$ containing the Selberg class is equivalent to a certain integral expression of the real part of the generalized Li coefficient $lambda_F(n)$ associated to $Finmathcal{S}^{sharpflat}$, for positive integers $n$. Moreover, we deduce that the GRH is equivalent to a certain expression of $Re(lambda_F(n))$ in terms of the sum of the Chebyshev polynomials of the first kind. Then, we partially evaluate the integral expression and deduce further relations equivalent to the GRH involving the generalized Euler-Stieltjes constants of the second kind associated to $F$. The class $mathcal{S}^{sharpflat}$ unconditionally contains all automorphic $L$-functions attached to irreducible cuspidal unitary representations of $GL_N(mathbb{Q})$, hence, as a corollary we also derive relations equivalent to the GRH for automorphic $L$-functions." @default.
- W4299364458 created "2022-10-02" @default.
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- W4299364458 date "2015-11-14" @default.
- W4299364458 modified "2023-10-09" @default.
- W4299364458 title "On relations equivalent to the generalized Riemann hypothesis for the Selberg class" @default.
- W4299364458 doi "https://doi.org/10.48550/arxiv.1511.04603" @default.
- W4299364458 hasPublicationYear "2015" @default.
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