The Riemann Zeta Function and the Spectral Zeta Function of Graphs

Diplôme Master The Riemann Zeta Function and the Spectral Zeta Function of Graphs eng 2022-08 author Pallich Massimiliano Carlo 876425 director Karlsson Anders 0000-0002-1886-6780 714906 65 In the first chapter, we recall and study the main classical results of the Riemann zeta function. Then in the second chapter, we focus on the connection between this latter and the prime numbers, by showing the Riemann explicit formula, and by showing for completeness the Von Mangoldt explicit formula. Finally in the last chapter, we first see the preliminary notions necessary to introduce the quite recent definition of the spectral zeta function of a graph and we recall in details some of the results already found. We will then use the first and second chapters to find similar structures and analogies between the Riemann zeta function and the spectral zeta function. In particular, we will make new graphs of these functions, find some new formulas and conjectures, and find some new special values and verify those already found. Number theory Riemann zeta function Spectral zeta function Power sums of sine Dewey 510 MSc in Mathematics 25 Section de mathématiques 11 false a2261164-21ee-4f4b-90fd-4b762b1d56be Master thesis Restricted Master thesis.pdf 1414426 application/pdf restrictedAccess Faculté des sciences / Section de mathématiques

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The Riemann Zeta Function and the Spectral Zeta Function of Graphs				2022	174	12

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Pallich, Massimiliano Carlo

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