Regularized product for the zeros of \(L\)-functions in the Selberg class (Q2839718)

The main result of this paper is an explicit formula for the regularized product of the non trivial zeros of \(L\)-functions in the Selberg class with a polynomial Euler product in terms of Milnor-gamma functions and poly \(L\)-functions defined by certain Euler products involving polylogarithms. The proof relies essentially on Weil's explicit formulas and the method developed by Deninger in the particular case of the Riemann zeta function.NEWLINENEWLINEThese results continue the investigations of \textit{C. Deninger} [Invent. Math. 107, 135--150 (1992; Zbl 0762.14015)], \textit{G. Illies} [Commun. Math. Phys. 220, No. 1, 69--94 (2001; Zbl 1025.58012)], \textit{M. Schröter} and \textit{C. Soulé} [Proc. Symp. Pure Math. 55, Pt. 1, 745--747 (1994; Zbl 0809.11045)] and \textit{A. Voros} [Commun. Math. Phys. 110, 439--465 (1987; Zbl 0631.10025)]. Furthermore, a new reformulation of the Riemann hypothesis is given.