Modeling families of L-functions

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.

References in corpus (4)

• 1- and 2-Level Densities for Rational Families of Elliptic Curves: Evidence for the Underlying Group Symmetries
• Lower-Order Terms of the 1-Level Density of Families of Elliptic Curves
• Derivatives of random matrix characteristic polynomials with applications to elliptic curves
• Applications of the L-functions ratios conjectures

Cited by in corpus (2)

• Moments of the critical values of families of elliptic curves, with applications
• Investigations of Zeros Near the Central Point of Elliptic Curve L-Functions