• Corpus ID: 117428676

Multiplicity one for $L$-functions and applications

  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},
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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