General Ω-theorems for coefficients of 𝐿-functions

Kaczorowski, Jerzy; Perelli, Alberto

doi:10.1090/proc/12652

General $\Omega$-theorems for coefficients of $L$-functions
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Proc. Amer. Math. Soc. 143 (2015), 5139-5145 Request permission

Abstract:

We prove a general $\Omega$-theorem for the coefficients of polynomial combinations of $L$-functions from the Selberg class. As a consequence, we show that the real and imaginary parts of any linear combination of coefficients of such $L$-functions have infinitely many sign changes, provided some simple necessary conditions are satisfied.

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