Topics in Number Theory: In Honor of B. Gordon and S. Chowla / Edition 1

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This volume contains the proceedings of the Topics in Number Theory Conference held at the Pennsylvania State University from July 31 through August 3, 1997. It contains seventeen research papers covering many areas of number theory; among them are contributions from four of the eight plenary speakers

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Editorial Reviews

The proceedings of the August 1997 conference contains 17 research papers reporting recent, significant work in many areas of number theory. The contributions from three of the plenary speakers are titled: motivating the multiplicative spectrum, modular Mahler measures, and the role of additive number theory in diophantine problems in many variable. Other topics are a fundamental invariant in the theory of partitions, a new minor-arcs estimate for number fields, Hecke characters and formal group characters, theorems and conjectures involving rook polynomials with only real zeros, and the divisibility of the specialization map for twists of abelian varieties. No index. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780792355830
  • Publisher: Springer US
  • Publication date: 3/31/1999
  • Series: Mathematics and Its Applications (closed) Series, #467
  • Edition description: 1999
  • Edition number: 1
  • Pages: 264
  • Product dimensions: 6.50 (w) x 9.56 (h) x 0.81 (d)

Table of Contents

Motivating the multiplicative spectrum 1
Modular Mahler measures I 17
Diophantine problems in many variables: The role of additive number theory 49
Equations F(x, y, a[superscript x]) = 0 85
A fundamental invariant in the theory of partitions 101
Congruence properties of values of L-functions and applications 115
On Tschirnhaus transformations 127
Hecke operators and the nonvanishing of L-functions 143
A new minor-arcs estimate for number fields 151
Modular functions, Maple and Andrews' tenth problem 163
Hecke characters and formal group characters 181
On certain Gauss periods with common decomposition field 193
Theorems and conjectures involving rook polynomials with only real zeros 207
An example of an elliptic curve with a positive density of prime quadratic twists which have rank zero 223
Exponents of class groups of quadratic fields 229
A local-global principle for densities 241
Divisibility of the specialization map for twists of abelian varieties 245
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