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Analytic Number Theory

In Honor of Helmut Maier’s 60th Birthday

  • Book
  • © 2015

Overview

Editors:
  1. Carl Pomerance

    1. Department of Mathematics, Dartmouth College, Hanover, USA

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  2. Michael Th. Rassias

    1. Department of Mathematics, ETH-Zürich, Zürich, Switzerland

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  • Presents the latest developments and applications by leading experts in Analytic Number Theory

  • Contains contributions by mathematicians who have published jointly with Helmut Maier

  • Contains practical material for graduate students and research mathematicians, as well as for computer scientists and engineers

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. CM-Points on Straight Lines

    • Bill Allombert, Yuri Bilu, Amalia Pizarro-Madariaga
    Pages 1-18

  3. Maass Waveforms and Low-Lying Zeros

    • Levent Alpoge, Nadine Amersi, Geoffrey Iyer, Oleg Lazarev, Steven J. Miller, Liyang Zhang
    Pages 19-55

  4. Théorème de Jordan Friable

    • Régis de la Bretèche, Gérald Tenenbaum
    Pages 57-64

  5. On Conjectures of T. Ordowski and Z.W. Sun Concerning Primes and Quadratic Forms

    • Christian Elsholtz, Glyn Harman
    Pages 65-81

  6. Large Gaps Between Consecutive Prime Numbers Containing Perfect Powers

    • Kevin Ford, D. R. Heath-Brown, Sergei Konyagin
    Pages 83-92

  7. On the Parity of the Number of Small Divisors of n

    • Kevin Ford, Florian Luca, Carl Pomerance, Jeffrey Shallit
    Pages 93-100

  8. Counting Primes in Arithmetic Progressions

    • John B. Friedlander
    Pages 101-114

  9. Limit Points of the Sequence of Normalized Differences Between Consecutive Prime Numbers

    • Daniel A. Goldston, Andrew H. Ledoan
    Pages 115-125

  10. Spirals of the Zeta Function I

    • Steven M. Gonek, Hugh L. Montgomery
    Pages 127-131

  11. Best Possible Densities of Dickson m-Tuples, as a Consequence of Zhang–Maynard–Tao

    • Andrew Granville, Daniel M. Kane, Dimitris Koukoulopoulos, Robert J. Lemke Oliver
    Pages 133-144

  12. A Note on Helson’s Conjecture on Moments of Random Multiplicative Functions

    • Adam J. Harper, Ashkan Nikeghbali, Maksym Radziwiłł
    Pages 145-169

  13. Large Values of the Zeta-Function on the Critical Line

    • Aleksandar Ivić
    Pages 171-194

  14. A Note on Bessel Twists of L-Functions

    • J. Kaczorowski, A. Perelli
    Pages 195-200

  15. The Sound of Fractal Strings and the Riemann Hypothesis

    • Michel L. Lapidus
    Pages 201-252

  16. Sums of Two Squares in Short Intervals

    • James Maynard
    Pages 253-273

  17. Infinite Sumsets with Many Representations

    • Melvyn B. Nathanson
    Pages 275-283

  18. On the Ratio of Consecutive Gaps Between Primes

    • János Pintz
    Pages 285-304

  19. Remarks on Fibers of the Sum-of-Divisors Function

    • Paul Pollack
    Pages 305-320

  20. On Amicable Numbers

    • Carl Pomerance
    Pages 321-327
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Keywords

About this book

This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and  trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler’s totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource.

Contributors to this volume:

Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang.

Editors and Affiliations

  • Department of Mathematics, Dartmouth College, Hanover, USA

    Carl Pomerance

  • Department of Mathematics, ETH-Zürich, Zürich, Switzerland

    Michael Th. Rassias

Bibliographic Information

  • Book Title: Analytic Number Theory

  • Book Subtitle: In Honor of Helmut Maier’s 60th Birthday

  • Editors: Carl Pomerance, Michael Th. Rassias

  • DOI: https://doi.org/10.1007/978-3-319-22240-0

  • Publisher: Springer Cham

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

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-22239-4Published: 28 November 2015

  • Softcover ISBN: 978-3-319-35551-1Published: 23 August 2016

  • eBook ISBN: 978-3-319-22240-0Published: 18 November 2015

  • Edition Number: 1

  • Number of Pages: VIII, 379

  • Topics: Number Theory, Numerical Analysis, Data Structures and Information Theory

  • Industry Sectors: IT & Software

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