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arXiv · 1305.3972

Multiplicity one for $L$-functions and applications

David W. Farmer·Ameya Pitale·Nathan C. Ryan·Ralf Schmidt
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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 $L$-functions. These results follow from our main result, which has slightly weaker hypotheses than previous multiplicity one theorems for $L$-functions. Significantly stronger results are available when the L-function is known to be automorphic.

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David W. Farmer, Ameya Pitale, Nathan C. Ryan, Ralf Schmidt. 2013-05-17. Multiplicity one for $L$-functions and applications. https://arxiv.org/abs/1305.3972

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