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1. 11. 2015.
On the modified Li criterion for a certain class of L-functions ☆
Abstract We define modified Li coefficients, called τ-Li coefficients for a very broad class S ♯ ♭ ( σ 0 , σ 1 ) of L-functions that contains the Selberg class, the class of all automorphic L-functions and the Rankin–Selberg L-functions, as well as products of suitable shifts of those functions. We prove the generalized Li criterion for zero-free regions of functions belonging to the class S ♯ ♭ ( σ 0 , σ 1 ) , derive an arithmetic formula for the computation of τ-Li coefficients and conduct numerical investigation of τ-Li coefficients for a certain product of shifts of the Riemann zeta function.