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arXiv · 2001.09274

Joint Extreme values of $L$-functions

Kamalakshya Mahatab·Łukasz Pańkowski·Akshaa Vatwani
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Abstract

We consider $L$-functions $L_1,\ldots,L_k$ from the Selberg class which have polynomial Euler product and satisfy Selberg's orthonormality condition. We show that on every vertical line $s=\sigma+it$ with $\sigma\in(1/2,1)$, these $L$-functions simultaneously take large values of size $\exp\left(c\frac{(\log t)^{1-\sigma}}{\log\log t}\right)$ inside a small neighborhood.

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Kamalakshya Mahatab, Łukasz Pańkowski, Akshaa Vatwani. 2020-01-25. Joint Extreme values of $L$-functions. https://arxiv.org/abs/2001.09274

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