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  • © 2015

Analytic Number Theory

In Honor of Helmut Maier’s 60th Birthday

  • 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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eBook USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-22240-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 109.99
Price excludes VAT (USA)
Hardcover Book USD 119.99
Price excludes VAT (USA)

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-viii
  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. Large Gaps Between Consecutive Prime Numbers Containing Perfect Powers

    • Kevin Ford, D. R. Heath-Brown, Sergei Konyagin
    Pages 83-92
  6. On the Parity of the Number of Small Divisors of n

    • Kevin Ford, Florian Luca, Carl Pomerance, Jeffrey Shallit
    Pages 93-100
  7. Counting Primes in Arithmetic Progressions

    • John B. Friedlander
    Pages 101-114
  8. Spirals of the Zeta Function I

    • Steven M. Gonek, Hugh L. Montgomery
    Pages 127-131
  9. 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
  10. A Note on Helson’s Conjecture on Moments of Random Multiplicative Functions

    • Adam J. Harper, Ashkan Nikeghbali, Maksym Radziwiłł
    Pages 145-169
  11. A Note on Bessel Twists of L-Functions

    • J. Kaczorowski, A. Perelli
    Pages 195-200
  12. Sums of Two Squares in Short Intervals

    • James Maynard
    Pages 253-273
  13. Infinite Sumsets with Many Representations

    • Melvyn B. Nathanson
    Pages 275-283
  14. On Amicable Numbers

    • Carl Pomerance
    Pages 321-327

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.

Keywords

  • Analytic number theory
  • Cyclotomic polynomials
  • Euler’s totient function
  • Möbius function
  • Riemann zeta function
  • Trigonometric sums

Editors and Affiliations

  • Department of Mathematics, Dartmouth College, Hanover, USA

    Carl Pomerance

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

    Michael Th. Rassias

Bibliographic Information

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-22240-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 109.99
Price excludes VAT (USA)
Hardcover Book USD 119.99
Price excludes VAT (USA)