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From Arithmetic to Zeta-Functions

Number Theory in Memory of Wolfgang Schwarz

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  • © 2016

Overview

Editors:
  1. Jürgen Sander

    1. Institut für Mathematik und Angewandte Informatik, Stiftung Universität Hildesheim, Hildesheim, Germany

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  2. Jörn Steuding

    1. Institut für Mathematik, Julius-Maximilians Universität Würzburg, Würzburg, Germany

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  3. Rasa Steuding

    1. Institut für Mathematik, Julius-Maximilians Universität Würzburg, Würzburg, Germany

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  • Offers a unique collection of interesting research and survey articles on modern aspects of elementary and analytic number theory

  • Collects several contributions which highlight Wolfgang Schwarz’s mathematics and life

  • Includes a few contributions which focus on historical aspects of certain number theoretical themes

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Table of contents (32 chapters)

  1. Front Matter

    Pages i-xxxvii
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  2. Forbidden Integer Ratios of Consecutive Power Sums

    • Ioulia N. Baoulina, Pieter Moree
    Pages 1-30

  3. A Note on the Negative Pell Equation

    • Valentin Blomer
    Pages 31-40

  4. Localisation Conditionnelle de Diviseurs

    • Régis de la Bretèche, Gérald Tenenbaum
    Pages 41-55

  5. A Ternary Problem in Additive Prime Number Theory

    • Jörg Brüdern
    Pages 57-81

  6. An Improvement of Liouville’s Inequality

    • Yann Bugeaud
    Pages 83-90

  7. Guided by Schwarz’ Functions: A Walk Through the Garden of Mahler’s Transcendence Method

    • Peter Bundschuh, Keijo Väänänen
    Pages 91-101

  8. Sums of Two Squares and a Power

    • Rainer Dietmann, Christian Elsholtz
    Pages 103-108

  9. Multiplicative Functions and the Sign of Maass Form Fourier Coefficients

    • Peter D. T. A Elliott
    Pages 109-120

  10. On Error Sum Functions for Approximations with Arithmetic Conditions

    • Carsten Elsner
    Pages 121-140

  11. Sum of the Lerch Zeta-Function over Nontrivial Zeros of the Dirichlet \(\boldsymbol{L}\)-Function

    • Ramūnas Garunkštis, Justas Kalpokas
    Pages 141-153

  12. Schur–Weyl Dualities Old and New

    • Anne Henke
    Pages 155-177

  13. Arithmetic Functions: A Pivotal Topic in the Scientific Work of Wolfgang Schwarz

    • Karl-Heinz Indlekofer
    Pages 179-199

  14. On Some Selected Works of Wolfgang Schwarz

    • Aleksandar Ivić
    Pages 201-216

  15. Sums of Two Squares of Sums of Two Squares

    • Rebecca Ulrike Jakob
    Pages 217-230

  16. The Joint Discrete Universality of Periodic Zeta-Functions

    • Antanas Laurinčikas
    Pages 231-246

  17. Remembering Wolfgang Schwarz, His Life and Work

    • Lutz G. Lucht
    Pages 247-261

  18. Dynamical Systems and Uniform Distribution of Sequences

    • Manfred G. Madritsch, Robert F. Tichy
    Pages 263-276

  19. Asymptotics and Equidistribution of Cotangent Sums Associated with the Estermann and Riemann Zeta Functions

    • Helmut Maier, Michael Th. Rassias
    Pages 277-293

  20. A Turán-Kubilius Inequality on Mappings of a Finite Set

    • Eugenijus Manstavičius
    Pages 295-307
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Keywords

About this book

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.

Editors and Affiliations

  • Institut für Mathematik und Angewandte Informatik, Stiftung Universität Hildesheim, Hildesheim, Germany

    Jürgen Sander

  • Institut für Mathematik, Julius-Maximilians Universität Würzburg, Würzburg, Germany

    Jörn Steuding, Rasa Steuding

About the editors

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. 


Bibliographic Information

  • Book Title: From Arithmetic to Zeta-Functions

  • Book Subtitle: Number Theory in Memory of Wolfgang Schwarz

  • Editors: Jürgen Sander, Jörn Steuding, Rasa Steuding

  • DOI: https://doi.org/10.1007/978-3-319-28203-9

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-28202-2Published: 06 January 2017

  • Softcover ISBN: 978-3-319-80296-1Published: 07 July 2018

  • eBook ISBN: 978-3-319-28203-9Published: 29 December 2016

  • Edition Number: 1

  • Number of Pages: XXXVII, 538

  • Number of Illustrations: 22 b/w illustrations, 45 illustrations in colour

  • Topics: Number Theory, Sequences, Series, Summability, History of Mathematical Sciences

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