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Number Theory and Analysis

A Collection of Papers in Honor of Edmund Landau (1877–1938)

  • Book
  • © 1969

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Editors:
  1. Paul Turán
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Table of contents (23 chapters)

  1. Front Matter

    Pages 1-8
    Download chapter PDF

  2. On the Large Sieve Method

    • E. Bombieri, H. Davenport
    Pages 9-22

  3. Über Binäre Additive Probleme Gemischter Art

    • B. M. Bredihin, J. V. Linnik, N. G. Tschudakoff
    Pages 23-37

  4. How to Extend A Calculus

    • J. G. Van Der Corput
    Pages 39-47

  5. On the Representation of Positive Integers as Sums of Three Cubes of Positive Rational Numbers

    • H. Davenport, E. Landau
    Pages 49-53

  6. Analytische Klassenzahlformeln

    • M. Deuring
    Pages 55-75

  7. Über Folgen Ganzer Zahlen

    • P. Erdős, A. Sárközi, E. Szemerédi
    Pages 77-86

  8. On the Average Length of a Class of Finite Continued Fractions

    • H. Heilbronn
    Pages 87-96

  9. Interpolation Analytischer Funktionen Auf Dem Einheitskreis

    • E. Hlawka
    Pages 97-118

  10. On the High-Indices Theorem for Borel Summability

    • A. E. Ingham
    Pages 119-135

  11. Bemerkungen Zu Landauschen Methoden in Der Gitterpunktlehre

    • V. Jarník
    Pages 137-156

  12. Über Einige Fragen Der Vergleichenden Primzahltheorie

    • S. Knapowski, P. Turán
    Pages 157-171

  13. On Local Theorems for Additive Number-Theoretic Functions

    • J. Kubilius
    Pages 173-191

  14. The “Pits Effect” for the Integral Function\(f\left( z \right) = \sum {\exp \left\{ { - {\vartheta ^{ - 1}}\left( {n\log n - n} \right) + \pi i\alpha {n^2}} \right\}{z^n},\alpha = \tfrac{1}{2}\left( {\sqrt 5 - 1} \right)} \)

    • J. E. Littlewood
    Pages 193-215

  15. On Numbers which can be Expressed as a Sum of Powers

    • L. J. Mordell
    Pages 217-221

  16. On Some Diophantine Equations y2 = x3 + k with no Rational Solutions (II)

    • L. J. Mordell
    Pages 223-232

  17. Über Das Vorzeichen Des Restgliedes im Primzahlsatz

    • G. Pólya
    Pages 233-244

  18. A Measure for the Differential-Transcendence of the Zeta-Function of Riemann

    • J. Popken
    Pages 245-255

  19. Comments on Euler’s “De Mirabilibus Proprietatibus Numerorum Pentagonalium”

    • H. Rademacher
    Pages 257-268

  20. On the Distribution of Numbers Prime to n

    • A. Rényi
    Pages 269-278
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Keywords

About this book

February 14, 1968 marked the thirtieth year since the death of Edmund Landau. The papers of this volume are dedicated by friends, students, and admirers to the memory of this outstanding scholar and teacher. To mention but one side of his original and varied scientific work, the results and effects of which cannot be dis­ cussed here, Edmund Landau performed one of his greatest services in developing the analytic theory of prime numbers from a subject accessible only with great difficulty even to the initiated few to the general estate of mathematicians. With the exception of the work of Chebyshev, Riemann, and Mertens, before Landau the problems of this theory were attempted only in a number of papers which were filled with gaps and errors. These problems were such that even Gauss abandoned them after several attempts in his youth, and they were described by N. H. Abel in a letter of 1823 and by O. Toeplitz in a lecture in 1930 as the deepest part of mathe­ matics. Clarification first began with the papers of Hadamard, de la Vallee Poussin, and von Mangoldt. At the end ofthe foreword to his work" Handbuch der Lehre von der Verteilung der Primzahlen" which appeared in 1909, Landau could thus remark with complete justification: " . . . The difficulty of the previously unsolved problems has frightened nearly everyone away from the theory of prime numbers.

Bibliographic Information

  • Book Title: Number Theory and Analysis

  • Book Subtitle: A Collection of Papers in Honor of Edmund Landau (1877–1938)

  • Editors: Paul Turán

  • DOI: https://doi.org/10.1007/978-1-4615-4819-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1969

  • Hardcover ISBN: 978-0-306-30384-5Due: 01 January 1999

  • Softcover ISBN: 978-1-4613-7184-7Published: 27 December 2011

  • eBook ISBN: 978-1-4615-4819-5Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: 356

  • Number of Illustrations: 3 b/w illustrations

  • Topics: Number Theory

  • Industry Sectors: IT & Software

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