Compatibility of Special value conjectures with the functional equation of Zeta functions

2020/05/11 by Flach, Matthias, Morin, Baptiste
#11G40 #14F20 (primary) 14F42 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.04829

Abstract

We prove that the special value conjecture for the Zeta function of a proper, regular arithmetic scheme X that we formulated in our previous article [8] is compatible with the functional equation of the Zeta function provided that the factor C(X,n) we were not able to compute in loc. cit. has the simple explicit form suggested in [9].

Related

• Some notes about the Zeta function and the Riemann hypothesis
• The functional equation for ζ
• The constant in the functional equation and derived extrior powers
• Special Values of Zeta Functions of Schemes
• Counting and zeta functions over F1