Eisenstein series twisted by modular symbols for the group SL(n)

TL;DR

This paper introduces a new class of Eisenstein series twisted by modular symbols for SL(n), proving their convergence in certain regions and providing explicit examples for SL(2) and SL(3).

Contribution

It generalizes previous constructions of Eisenstein series by incorporating modular symbols for higher rank groups like SL(n).

Findings

Convergence of twisted Eisenstein series in a specific cone.

Explicit examples for SL(2) and SL(3).

Extension of Eisenstein series theory to include modular symbols.

Abstract

We define Eisenstein series twisted by modular symbols on the group SL(n), generalizing a construction of the first author. We show that, in the case of series attached to the minimal parabolic subgroup, our series converges for all points in a suitable cone. We conclude with examples for SL(2) and SL(3).