# Multiplicity one for $L$-functions and applications

@article{Farmer2013MultiplicityOF, title={Multiplicity one for \$L\$-functions and applications}, author={David W. Farmer and Ameya Pitale and Nathan C. Ryan and Ralf Schmidt}, journal={arXiv: Number Theory}, year={2013} }

We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients satisfy a partial Ramanujan bound and do not differ by too much. Additionally, we prove a number of multiplicity one type results for the number-theoretic objects attached to $L$-functions. These results follow from our main result about $L$-functions.

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