SHARP UPPER BOUNDS FOR FRACTIONAL MOMENTS OF THE RIEMANN ZETA FUNCTION

By W. Heap, Maksym Radziwill, Kannan Soundararajan. Quarterly Journal of Mathematics, 2019

47 citations recorded by the source corpus.

We establish sharp upper bounds for the $2k$th moment of the Riemann zeta function on the critical line, for all real $0 \leqslant k \leqslant 2$. This improves on earlier work of Ramachandra, Heath-Brown and Bettin–Chandee–Radziwiłł.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d427e51a10dd3fb8b1953805c30bcf63dd76cbb9

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

In Discrete Mathematics and Combinatorics

1. Kannan Soundararajan
2. M. Young
3. Paul D. Nelson

In Geometry and Topology

1. W. Heap
2. Kannan Soundararajan
3. Adam J Harper
4. Christoph Aistleitner
5. P. Bourgade
6. Maksym Radziwill
7. Alexandra Florea
8. Yitang Zhang

Citations in the corpus

• Lower bounds for moments of zeta and $L$-functions revisited (2020, background): “Recent work of the authors with Radziwi l l [3] provides such upper bounds for all moments of the Riemann zeta-function below the fourth moment.”