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Washington State
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Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

Meet on Zoom

https://wsu.zoom.us/j/95294405915?pwd=MmhnVFBvOW5DSkdMYWJqbWhQM1NXQT09

Meeting ID: 952 9440 5915

Password: M410

November 14, Monday, 4:10 - 5:00 PM

Nathan Ng

Department of Mathematics and Computer Science

University of Lethbridge

Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

Meet on Zoom

https://wsu.zoom.us/j/95294405915?pwd=MmhnVFBvOW5DSkdMYWJqbWhQM1NXQT09

Meeting ID: 952 9440 5915

Password: M410

November 14, Monday, 4:10 - 5:00 PM

Nathan Ng

Department of Mathematics and Computer Science

University of Lethbridge

Title: Moments of the Riemann Zeta Function

Abstract: For over 100 years, $I_k(T)$, the $2k$-th moments of the Riemann zeta function on the critical line, have been extensively studied. In 1918 Hardy-Littlewood established an asymptotic formula for the second moment ($k=1$) and in 1926 Ingham established an asymptotic formula for the fourth moment ($k=2$). Since then, no other moments have been asymptotically evaluated. In the late 1990's Keating and Snaith gave a conjecture for the size of $I_k(T)$ based on a random matrix model. In this talk I will give a historical overview of the advances on $I_k(T)$ and the techniques used to study them since the beginning of the twentieth century.

Abstract: For over 100 years, $I_k(T)$, the $2k$-th moments of the Riemann zeta function on the critical line, have been extensively studied. In 1918 Hardy-Littlewood established an asymptotic formula for the second moment ($k=1$) and in 1926 Ingham established an asymptotic formula for the fourth moment ($k=2$). Since then, no other moments have been asymptotically evaluated. In the late 1990's Keating and Snaith gave a conjecture for the size of $I_k(T)$ based on a random matrix model. In this talk I will give a historical overview of the advances on $I_k(T)$ and the techniques used to study them since the beginning of the twentieth century.