From Arithmetic to Zeta-Functions (eBook)

Jürgen Sander is professor at the Department of Mathematics, University of Hildesheim, Germany.Jörn Steuding is professor at the Department of Mathematics, University of Würzburg, Germany. Dr. Rasa Steuding is a researcher at the Department of Mathematics, University of Würzburg, Germany. 

Preface.- Forbidden Integer Ratios of Consecutive Power Sums, Ioulia N. Baoulina and Pieter Moree.- A Note on the Negative Pell Equation, Valentin Blomer.- Localisation Conditionnelle de Diviseurs, Régis de la Bretèche, Gérald Tenenbaum.- A Ternary Problem in Additive Prime Number Theory, Jörg Brüdern.- An Improvement of Liouville’s Inequality, Yann Bugeaud.- Guided by Schwarz’ Functions: a Walk Through the Garden of Mahlers Transcendence Method, Peter Bundschuh and Keijo Väänänen.- Sums of Two Squares and a Power, Rainer Dietmann and Christian Elsholtz.- Multiplicative Functions and the Sign of Maass Form Fourier Coefficients, P. D. T. A. Elliott.- On Error Sum Functions for Approximations with Arithmetic Conditions, Carsten Elsner.- Sum of the Lerch Zeta Function over Nontrivial Zeros of the Dirichlet L-Function, Ramūnas Garunkštis and Justas Kalpokas.- Schur-Weyl-Dualities - Old and New, Anne Henke.- Arithmetic functions - a Pivotal Topic in the Scientific Work of Wolfgang, Karl-Heinz Indlekofer.- On Some Selected Works of Wolfgang Schwarz, Aleksandar Ivić.- Sums of Two Squares of Sums of Two Squares, Rebecca Jakob.- The Joint Discrete Universality of Periodic Zeta-Functions, Antanas Laurinčikas.- Remembering Wolfgang Schwarz, his Life and Work, Lutz G. Lucht.- Dynamical Systems and Uniform Distribution of Sequences, Manfred G. Madritsch and Robert F. Tichy.- Asymptotics and Equidistribution of Cotangent Sums Associated to the Estermann and Riemann Zeta Functions, Helmut Maier and Michael Th. Rassias.- A Turán-Kubilius Inequality on Mappings of a Finite Set, Eugenijus Manstavičius.- Aspects of Zeta-Function Theory in the Mathematical Works of Adolf Hurwitz, Nicola M.R. Oswald and Jörn Steuding.- Selberg Sums a New Perspective, Samuel J. Patterson.- Polignac Numbers, Conjectures of Erdős on Gaps between Primes, Arithmetic Progressions in Primes, and the Bounded Gap Conjecture, János Pintz.- Idempotents and Congruence ax=b (mod n), Štefan Porubský.- Recent Developments on the Edge Between Number Theory and Graph Theory, Jürgen Sander and Thorsten Sander.- The Leading Coefficients of Stern Polynomials, Andrzeij Schinzel.- The Non-Existence of Universal Carmichael Numbers, Jan-Christoph Schlage-Puchta.- Arithmetic Properties of Blocks of Consecutive Integers, Tarlok N. Shorey and Rob Tijdeman.- The GCD of the Shifted Fibonacci Sequence, Jürgen Spilker.- On Liouville Numbers - Yet Another Application of Functional Analysis to Number Theory, Jörn Steuding.- Natural Boundaries of Power Series with Multiplicative Coefficients in Algebraic Number Fields, Friedemann Tuttas.- A Minimal Result of Hardy, Eduard Wirsing.- Regular Dessins with Abelian Automorphism Groups, Jürgen Wolfart and Benjamin Mühlbauer.