Combinations of $L$-functions and Their Non-coincident Zeros for $\sigma>1$

Abstract

The purpose of this note is to build upon work of Booker--Thorne and Righetti concerning zeros of algebraic combinations of $L$-functions. Namely, we show that two generic combinations of functions from a wide class of Euler products have non-coincident zeros in the half-plane $\sigma>1$.Comment: 6 page