On poles of twisted tensor L-functions

TL;DR

This paper proves that for all quadratic extensions of global fields, the only potential pole of twisted tensor L-functions in the region Re(s) ≥ 1 occurs at s=1, clarifying their analytic behavior.

Contribution

It establishes a precise location for poles of twisted tensor L-functions over quadratic extensions, advancing understanding of their analytic properties.

Findings

Pole at s=1 is the only possible in Re(s) ≥ 1 for these L-functions.

Confirms no other poles exist in the specified region.

Results apply uniformly across all quadratic extensions of global fields.

Abstract

It is shown that the only possible pole of the twisted tensor L-functions in Re(s)\geq 1 is located at s=1 for all quadratic extensions of global fields.