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arXiv · 1608.07887

An extremal problem related to generalizations of the Nyman-Beurling and B\'aez-Duarte criteria

Dimitar K. Dimitrov·Willian D. Oliveira
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Abstract

We establish generalizations of the Nyman-Beurling and B\'aez-Duarte criteria concerning lack of zeros of Dirichlet $L$-functions in the semi-plane $\Re(s) >1/p$ for $p\in (1,2]$. We pose and solve a natural extremal problem for Dirichlet polynomials which take values one at the zeros of the corresponding $L$-function on the vertical line $\Re(s)=1/p$.

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Dimitar K. Dimitrov, Willian D. Oliveira. 2016-08-29. An extremal problem related to generalizations of the Nyman-Beurling and B\'aez-Duarte criteria. https://arxiv.org/abs/1608.07887

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