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Topics in Number Theory

In Honor of B. Gordon and S. Chowla

  • Book
  • © 1999

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Editors:
  1. Scott D. Ahlgren

    1. Department of Mathematics, Pennsylvania State University, USA

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  2. George E. Andrews

    1. Department of Mathematics, Pennsylvania State University, USA

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  3. Ken Ono

    1. Department of Mathematics, Pennsylvania State University, USA

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Part of the book series: Mathematics and Its Applications (MAIA, volume 467)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-viii
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  2. Motivating the Multiplicative Spectrum

    • Andrew Granville, K. Soundararajan
    Pages 1-15

  3. Modular Mahler Measures I

    • F. Rodriguez Villegas
    Pages 17-48

  4. Diophantine Problems in Many Variables: The Role of Additive Number Theory

    • Trevor D. Wooley
    Pages 49-83

  5. Equations F(x,y,α x) = 0

    • Scott Ahlgren
    Pages 85-100

  6. A Fundamental Invariant in the Theory of Partitions

    • Krishnaswami Alladi
    Pages 101-113

  7. Congruence Properties of Values of L-Functions and Applications

    • J. H. Bruinier, K. James, W. Kohnen, K. Ono, C. Skinner, V. Vatsal
    Pages 115-125

  8. On Tschirnhaus Transformations

    • Joe Buhler, Zinovy Reichstein
    Pages 127-142

  9. Hecke Operators and the Nonvanishing of L—Functions

    • J. B. Conrey, D. W. Farmer
    Pages 143-150

  10. A New Minor-Arcs Estimate for Number Fields

    • Morley Davidson
    Pages 151-161

  11. Modular Functions, Maple and Andrews’ 10th Problem

    • Frank Garvan
    Pages 163-179

  12. Hecke Characters and Formal Group Characters

    • Li Guo
    Pages 181-192

  13. On certain Gauss periods with common decomposition field

    • S. Gurak
    Pages 193-205

  14. Theorems and Conjectures Involving Rook Polynomials with Only Real Zeros

    • James Haglund, Ken Ono, David G. Wagner
    Pages 207-221

  15. An Example of an Elliptic Curve with a Positive Density of Prime Quadratic Twists Which Have Rank Zero

    • Kevin James
    Pages 223-227

  16. Exponents of Class Groups of Quadratic Fields

    • M. Ram Murty
    Pages 229-239

  17. A Local-Global Principle for Densities

    • Bjorn Poonen, Michael Stoll
    Pages 241-244

  18. Divisibility of the Specialization Map for Twists of Abelian Varieties

    • Joseph H. Silverman
    Pages 245-258

  19. Back Matter

    Pages 259-263
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Keywords

About this book

From July 31 through August 3,1997, the Pennsylvania State University hosted the Topics in Number Theory Conference. The conference was organized by Ken Ono and myself. By writing the preface, I am afforded the opportunity to express my gratitude to Ken for beng the inspiring and driving force behind the whole conference. Without his energy, enthusiasm and skill the entire event would never have occurred. We are extremely grateful to the sponsors of the conference: The National Sci­ ence Foundation, The Penn State Conference Center and the Penn State Depart­ ment of Mathematics. The object in this conference was to provide a variety of presentations giving a current picture of recent, significant work in number theory. There were eight plenary lectures: H. Darmon (McGill University), "Non-vanishing of L-functions and their derivatives modulo p. " A. Granville (University of Georgia), "Mean values of multiplicative functions. " C. Pomerance (University of Georgia), "Recent results in primality testing. " C. Skinner (Princeton University), "Deformations of Galois representations. " R. Stanley (Massachusetts Institute of Technology), "Some interesting hyperplane arrangements. " F. Rodriguez Villegas (Princeton University), "Modular Mahler measures. " T. Wooley (University of Michigan), "Diophantine problems in many variables: The role of additive number theory. " D. Zeilberger (Temple University), "Reverse engineering in combinatorics and number theory. " The papers in this volume provide an accurate picture of many of the topics presented at the conference including contributions from four of the plenary lectures.

Editors and Affiliations

  • Department of Mathematics, Pennsylvania State University, USA

    Scott D. Ahlgren, George E. Andrews, Ken Ono

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