Zeros of $L$-functions in families near the critical line

Valentin Blomer; Jesse Thorner

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arXiv · 2410.17158

Zeros of $L$-functions in families near the critical line

Valentin Blomer·Jesse Thorner

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Abstract

We combine the relative trace formula with analytic methods to obtain zero density estimate for $L$-functions in various families of automorphic representations for $\mathrm{GL}(m)$. Applications include strong bounds for the average analytic rank of these $L$-functions at the central point and average equidistribution results for the imaginary parts of the zeros.

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Valentin Blomer, Jesse Thorner. 2024-10-22. Zeros of $L$-functions in families near the critical line. https://arxiv.org/abs/2410.17158

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