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Modeling families of L-functions

David W Farmer
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Abstract

We discuss the idea of a ``family of L-functions'' and describe various methods which have been used to make predictions about L-function families. The methods involve a mixture of random matrix theory and heuristics from number theory. Particular attention is paid to families of elliptic curve L-functions. We describe two random matrix models for elliptic curve families: the Independent Model and the Interaction Model.

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David W Farmer. 2005-11-04. Modeling families of L-functions. https://arxiv.org/abs/math/0511107

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