What question did this study set out to answer?

The aim is to establish conditions for when two Euler products of L-functions are identical based on their coefficients and functional equations.

March 29, 2026

Multiplicity one for analytic L -functions and applications

Key Points

The aim is to establish conditions for when two Euler products of L-functions are identical based on their coefficients and functional equations.
Proving conditions for identical Euler products under functional equations.
Analyzing coefficients' size and difference limitations.
Deriving multiplicity one results linked to L-functions.
Presented conditions yielding stronger multiplicity one results for certain L-functions.
Demonstrated weaker hypotheses compared to earlier multiplicity one theorems.
Stronger results achieved when L-functions are identified as automorphic.

Abstract

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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