From Arithmetic to Zeta-Functions

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.