Lower bounds for moments of L-functions: symplectic and orthogonal examples

By Z. Rudnick, Kannan Soundararajan. 2006

75 citations recorded by the source corpus.

We give lower bounds of the conjectured order of magnitude for an orthogonal and a symplectic family of L-functions.

Subfields: Algebra and Number Theory, Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7123e5e5152dcf8f54a88a3a9840a3652f08fa00

How researchers see this paper

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

In Algebra and Number Theory

1. Maksym Radziwill
2. Nathan Ng
3. Kannan Soundararajan
4. M. Young
5. Adam J Harper
6. Alexandra Florea
7. W. Heap
8. Paul D. Nelson

In Applied Mathematics

1. Nathan Ng
2. Maksym Radziwill
3. M. Young
4. Kannan Soundararajan
5. Christoph Aistleitner
6. Ian Petrow
7. Andriy V. Bondarenko
8. Kristian Seip

In Numerical Analysis

1. Nathan Ng
2. M. Young
3. Maksym Radziwill
4. Kannan Soundararajan

Citations in the corpus

• The second moment of quadratic twists of modular L-functions (2009, methodology): “For simplicity we have restricted attention to fundamental discriminants of the form 8d, but we may also handle similarly all discriminants.”
• Moments and distribution of central L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L$$\end{document}-values of quadr (2014, background): “Conditional on theGeneralized RiemannHypothesis, thework of Soundararajan [32] together with its sharp refinement by Harper [13] establishes the conjectured upper bounds for moments in many families; our work may be viewed as an unconditional analog of such results, but for a restricted range of mom”
• Extreme values of zeta and L-functions (2007, methodology): “Rudnick and the author ([11] and [12]) found a flexible method to obtain lower bounds for moments in many families of L-functions, but the bounds obtained here are superior.”
• Extreme values of ζ′(ρ) (2007, methodology): “Clearly, (1) implies Theorem 1. However, as this remains unpublished, we present our proof of Theorem 1. Thus under the Riemann hypothesis, the lower bound method [12], [ 13 ] can give omega results for ζ ′ (ρ) of the same strength as the resonance method”
• Moments of the Riemann zeta function (2006, background): “Analogous conjectures exist (see [2], [4], [11]) for moments of central values of L-functions in families, and in many cases lower bounds of the conjectured order are known (see [16] and [17]).”