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arXiv · 1506.07630

Some remarks on the convergence of the Dirichlet series of L-functions and related questions

J. Kaczorowski·A. Perelli
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Abstract

First we show that the abscissae of uniform and absolute convergence of Dirichlet series coincide in the case of $L$-functions from the Selberg class $\mathcal{S}$. We also study the latter abscissa inside the extended Selberg class, indicating a different behavior in the two classes. Next we address two questions about majorants of functions in $\mathcal{S}$, showing links with the distribution of the zeros and with independence results.

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J. Kaczorowski, A. Perelli. 2015-06-25. Some remarks on the convergence of the Dirichlet series of L-functions and related questions. https://arxiv.org/abs/1506.07630

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