CONTINUOUS LOWER BOUNDS FOR MOMENTS OF ZETA AND L -FUNCTIONS.
By Maksym Radziwill, Kannan Soundararajan. 2012
70 citations recorded by the source corpus.
We obtain lower bounds of the correct order of magnitude for the 2k-th moment of the Riemann zeta function for all k ‚ 1. Previously such lower bounds were known only for rational values of k, with the bounds depending on the height of the rational number k. Our new bounds are continuous in k, and thus extend also to the case when k is irrational. The method is a refinement of an approach of Rudnick and Soundararajan, and applies also to moments of L-functions in families.
Subfields: Algebra and Number Theory, Artificial Intelligence
View Paper: https://www.semanticscholar.org/paper/e0e34bc2207c4679e1d2575a7c3a6b25cb0292eb
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In Algebra and Number Theory
- Adam J Harper
- Maksym Radziwill
- W. Heap
- Kannan Soundararajan
- Alexandra Florea
- Joseph Najnudel
- L. Arguin
- Paul D. Nelson
In Artificial Intelligence
Citations in the corpus
- Lower bounds for moments of zeta and $L$-functions revisited (2020, background): “To place our result briefly in context, we recall that in the range k ≥ 1 such a lower bound was established by [7], although our quantification of Ck is better and the proof arguably simpler.”
- 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): “Furthermore, the work of Rudnick and Soundararajan ([27,28]), together with its extension by the authors in [25], produces lower bounds of the conjectured order of magnitude for all moments larger than the first, provided a little more than the first moment can be computed.”
- Sharp conditional bounds for moments of the Riemann zeta function (2013, methodology): “Theorem 1 is sharp up to the value of the implicit constant, since Radziwi l l and Soundararajan [13] have proved a matching lower bound unconditionally when k ≥ 1, and earlier Ramachandra (see [14, 15]) and Heath-Brown [6] proved a matching lower bound for all k ≥ 0, but assuming the Riemann…”