Multiplicity one for $L$-functions and applications
Number Theory
2025-05-13 v2
Abstract
We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients are not too large and do not differ from each other by too much. Additionally, we prove a number of multiplicity one type results for the number-theoretic objects attached to -functions. These results follow from our main result, which has slightly weaker hypotheses than previous multiplicity one theorems for -functions. Significantly stronger results are available when the L-function is known to be automorphic.
Cite
@article{arxiv.1305.3972,
title = {Multiplicity one for $L$-functions and applications},
author = {David W. Farmer and Ameya Pitale and Nathan C. Ryan and Ralf Schmidt},
journal= {arXiv preprint arXiv:1305.3972},
year = {2025}
}
Comments
Significant revision. Provides more motivation behind our approach and includes different applications