Distribution of values of $L$-functions at the edge of the critical strip

Abstract

We prove several results on the distribution of values of $L$-functions at the edge of the critical strip, by constructing and studying a large class of random Euler products. Among new applications, we study families of symmetric power $L$-functions of holomorphic cusp forms in the level aspect (assuming the automorphy of these $L$-functions) at $s=1$, functions in the Selberg class (in the height aspect), and quadratic twists of a fixed $GL(m)/\mathbb{Q}$-automorphic cusp form at $s=1$.

30 pages

References in corpus (1)

• Extreme values of $|\zeta (1+it)|$

Cited by in corpus (6)

• Effective log-free zero density estimates for automorphic $L$-functions and the Sato-Tate conjecture
• Large deviations for values of $L$-functions attached to cusp forms in the level aspect
• The value-distribution of Artin $L$-functions associated with cubic fields in conductor aspect
• The distribution of large quadratic character sums and applications
• On the distribution of large values of $|\zeta (1+\mathrm{i}t)|$
• Distribution of Values of Symmetric power L-functions at the Edge of the Critical Strip