The twisted fourth moment of the Riemann zeta function
66 citations recorded by the source corpus.
Abstract We compute the asymptotics of the fourth moment of the Riemann zeta function times an arbitrary Dirichlet polynomial of length .
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/8f6e6ac6d2079219627ae54c40ee832adb311557
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In Algebra and Number Theory
- W. Heap
- Maksym Radziwill
- M. Young
- Kannan Soundararajan
- Siegfred Baluyot
- Adam J Harper
- Alexandra Florea
- Paul D. Nelson
In Applied Mathematics
- Maksym Radziwill
- Siegfred Baluyot
- M. Young
- Kannan Soundararajan
- W. Heap
- Nathan Ng
- Christoph Aistleitner
- Ian Petrow
Citations in the corpus
- On the zeros of Riemann's zeta-function on the critical line (2016, methodology): “We prove this by applying the recent theorem of Hughes and Young [16].”
- SHARP UPPER BOUNDS FOR FRACTIONAL MOMENTS OF THE RIEMANN ZETA FUNCTION (2019, methodology): “Theorem 1 is an illustration of this principle, and combines the ideas of [10] together with knowledge of the fourth moment of ζ(s) twisted by short Dirichlet polynomials (see the work of Hughes and Young [7], and Betin, Bui, Li, and Radziwi l l [1]).”
- The quantum unique ergodicity conjecture for thin sets (2013, methodology): “re, via (2.9), (6.26) w(t) = cosh(πT) 23πα+β+γ+δ 2 Γ 1 2 +α+it 2 Γ 1 2 +β+it Γ 1 2 +γ− it 2 Γ 1 2 +δ− it . As stated in Theorem 7.1 below, (which is the large shift analog of Theorem 1.1 of [HY]), the main term2 of (6.24) is the sum of six terms. In this paper we shall extend this result to hold f”
- 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, unknown): “For the Riemann zeta-function, where the fourth moment (plus epsilon) is known (see [17]), we are thus able to establish sharp upper bounds for all moments below the fourth; previously such bounds were established by Heath-Brown [14] conditional on the Riemann Hypothesis.”