On the Density Hypothesis for the Selberg class

2024/08/01 by J. Pintz, Pintz, János
Mathematics · #Mathematical Approximation and Integration #Analytic and geometric function theory #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2408.00617

Abstract

We prove a general zero density theorem on the Selberg class of functions. The result verifies the Density Hypothesis in the strip when the real part of the variable is at least 0.9 under the assumption that the degree of the function does not exceed 2. In the other cases we obtain a density theorem weaker than the Density Hypothesis.

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