K\"ohler's Conjecture on Hecke Theta Series of Weight One

TL;DR

This paper proves K"ohler's conjecture regarding the ambiguity in quadratic fields for Hecke theta series of weight one by linking it to Galois representations induced from quadratic characters.

Contribution

It establishes a connection between K"ohler's conjecture and Galois representations, providing a proof for the ambiguity issue in Hecke theta series.

Findings

Proof of K"ohler's conjecture on Hecke theta series ambiguity

Link between quadratic fields and Galois representations

Clarification of the structure of weight one Hecke theta series

Abstract

In this article, we prove a conjecture of G\"unter K\"ohler on the ambiguity of the quadratic field in the definition of Hecke theta series by deriving it from a similar statement on two-dimensional Galois representations induced from characters of quadratic fields.