Introduction to: 1- and 2-Level Densities for Families of Elliptic Curves: Evidence for the Underlying Group Symmetries

By Steven J. Miller. 2003

81 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/26547016433d48167f4c1afa707dc89da54d4fa1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. M. Young
2. Steven J. Miller
3. Ian Petrow
4. Emmanuel Kowalski
5. Peter Sarnak
6. Stephan Baier
7. Manjul Bhargava
8. V. Blomer

Citations in the corpus

• Low-lying zeros of families of elliptic curves (2004, background): “φ(0) contribution. Obtaining these two theorems with the stated support crucially requires GRH for Dirichlet L-functions. 2ForusR+ =(0,∞) 3 SUMMARYOFMAINRESULTS 7 S. J. Miller, in his doctoral thesis [Mil], has independently proved density theorems for various families ofelliptic curves (alongwith o”
• A Symplectic Test of the L-Functions Ratios Conjecture (2007, background): “One example of this is that zeros at height T are modeled not by the N → ∞ scaling limits of a classical compact group but by matrices of size N ∼ log(T/2π) [31, 32, 33].”