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Topics in probabilistic number theory

Abstract:

In this work we explore three distinct problems on the interface of number theory and random matrix theory. First, we compute the average of two shifted squares of the Riemann zeta on the critical line with shifts up to size T 6/5−ε. We give an explicit expression for such averages as well as the (2, 2)-moment of moment of the Riemann zeta. Our result confirms a conjecture of Chandee as well as a special case of Motohashi’s integral. Our approach relies on correlations of the divisor function...

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Division:
MPLS
Department:
Mathematical Institute
Role:
Author

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Supervisor
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Name:
University of Oxford
Funder identifier:
http://dx.doi.org/10.13039/501100000769
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
Language:
English
Deposit date:
2023-02-06

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