From Arithmetic to Zeta-Functions

Number Theory in Memory of Wolfgang Schwarz

Jürgen Sander, Jörn Steuding, Rasa Steuding (Herausgeber)

Buch | Hardcover

XXXVII, 538 Seiten

2017 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-28202-2 (ISBN)

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This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany. Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number theorist and cherished colleague Wolfgang Schwarz (1934-2013), who contributed over one hundred articles on number theory, its history and related fields. Readers interested in elementary or analytic number theory and related fields will certainly find many fascinating topical results among the contributions from both respected mathematicians and up-and-coming young researchers. In addition, some biographical articles highlight the life and mathematical works of Wolfgang Schwarz.

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, Ramunas Garunkstis 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 Ivic.- Sums of Two Squares of Sums of Two Squares, Rebecca Jakob.- The Joint Discrete Universality of Periodic Zeta-Functions, Antanas Laurincikas.- 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 Manstavicius.- 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 Erdös on Gaps between Primes, Arithmetic Progressions in Primes, and the Bounded Gap Conjecture, János Pintz.- Idempotents and Congruence ax=b (mod n), Stefan 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.

Erscheinungsdatum	24.01.2017
Zusatzinfo	XXXVII, 538 p. 67 illus., 45 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	arithmetical functions • diophantine approximation and diophantine equation • diophantine approximation and diophantine equations • History of mathematical sciences • mathematics and statistics • Number Theory • representation problems from additive number theor • representation problems from additive number theory • Sequences and sets • Sequences, Series, Summability • Zeta-functions
ISBN-10	3-319-28202-6 / 3319282026
ISBN-13	978-3-319-28202-2 / 9783319282022
Zustand	Neuware