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Noncommutative modular symbols and Eisenstein series

Research paper by Gautam Chinta, Ivan Horozov, Cormac O'Sullivan

Indexed on: 07 Apr '17Published on: 07 Apr '17Published in: arXiv - Mathematics - Number Theory



Abstract

We form real-analytic Eisenstein series twisted by Manin's noncommutative modular symbols. After developing their basic properties, these series are shown to have meromorphic continuations to the entire complex plane and satisfy functional equations in some cases. This theory neatly contains and generalizes earlier work in the literature on the properties of Eisenstein series twisted by classical modular symbols.