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Twisted second moments and explicit formulae of the Riemann zeta-function


Robles, Nicolas. Twisted second moments and explicit formulae of the Riemann zeta-function. 2015, University of Zurich, Faculty of Science.

Abstract

Several aspects connecting analytic number theory and the Riemann zeta-function are studied and expanded. These include:
1. explicit formulae relating the Möbius function to the non-trivial zeros of the zeta
function;
2. generalized results on sums of Ramanujan sums;
3. new results on the combinations of Riemann $\Xi$-functions on bounded vertical shifts and their zeros on the critical line;
4. a generalization of moment integrals involving the Riemann $\Xi$-function;
5. asymptotics for the mean square of the product of the Riemann $\xi$-function and new Dirichlet polynomials;
6. zeta regularization on tori and a new proof of the Chowla-Selberg formula.

Abstract

Several aspects connecting analytic number theory and the Riemann zeta-function are studied and expanded. These include:
1. explicit formulae relating the Möbius function to the non-trivial zeros of the zeta
function;
2. generalized results on sums of Ramanujan sums;
3. new results on the combinations of Riemann $\Xi$-functions on bounded vertical shifts and their zeros on the critical line;
4. a generalization of moment integrals involving the Riemann $\Xi$-function;
5. asymptotics for the mean square of the product of the Riemann $\xi$-function and new Dirichlet polynomials;
6. zeta regularization on tori and a new proof of the Chowla-Selberg formula.

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Additional indexing

Item Type:Dissertation
Referees:Cattaneo Alberto S, Nikeghbali Ashkan, Ayoub Joseph, Berndt Bruce
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2015
Deposited On:21 Jan 2016 12:50
Last Modified:08 Dec 2017 13:37
Number of Pages:170
Official URL:http://www.recherche-portal.ch/ZAD:default_scope:ebi01_prod010470417

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