Joint extreme values of $L$-functions

Abstract: We consider $L$-functions $L_1,\ldots,L_k$ from the Selberg class having polynomial Euler product and satisfying Selberg's orthonormality condition. We show that on every vertical line $s=\sigma+it$ in the complex plane with $\sigma \in(1/2,1)$, these $L$-functions simultaneously take "large" values inside a small neighborhood. Our method extends to $\sigma=1$ unconditionally, and to $\sigma =1/2$ on the generalized Riemann hypothesis. We also obtain similar joint omega results for arguments of the given $L$-functions. This is joint work with Kamalakshya Mahatab and Łukasz Pańkowski.

Mathematics

Audience: researchers in the topic

CRG Weekly Seminars

Series comments: These seminars will be centered on various topics in L-functions in analytic number theory. If you are interested, please register here to receive the Zoom link: uleth.zoom.us/meeting/register/tJ0ucO-spjkvEtGdqQv0rwzSYNjWjYBohVTu