Number Theory : New York Seminar 2003

by New York Number Theory Seminar; Chudnovsky, Gregory; Nathanson, Melvyn B.

• ISBN13: 9780387406558
• ISBN10: 0387406557
• Format: Hardcover
• Copyright: 2004-01-01
• Publisher: Springer Verlag

Summary

This volume marks the 20th anniversary of the New York Number Theory Seminar (NYNTS). Beginning in 1982, the NYNTS has tried to present a broad spectrum of research in number theory and related fields of mathematics, from physics to geometry to combinatorics and computer science. The list of seminar speakers includes not only Fields Medallists and other established researchers, but also many other younger and less well known mathematicians whose theorems are significant and whose work may become the next big thing in number theory.

Table of Contents

Preface	v
1 The Spanning Number and the Independence Number of a Subset of an Abelian Group	1	(16)
Béla Bajnok
2 A Formula Related to the Frobenius Problem in Two Dimensions	17	(8)
Matthias Beck and Sinai Robins
3 One Bit World	25	(36)
David V. Chudnovsky and Gregory V. Chudnovsky
4 Use of Pad & Approximation in Spline Construction	61	(26)
David V. Chudnovsky and Gregory V. Chudnovsky
5 Interactions between Number Theory and Operator Algebras in the Study of the Riemann Zeta Function (d'aprés Bost-Connes and Connes)	87	(18)
Paula B. Cohen
6 A Hyperelliptic Curve with Real Multiplication of Degree Two	105	(28)
Harvey Cohn
7 Humbert's Conic Model and the Kummer Surface	133	(66)
Harvey Cohn
8 Arithmeticity and Theta Correspondence of an Orthogonal Group	199
Ze-Li Dou
9 Morphic Heights and Periodic Points	167	(12)
M. Einsiedler, G. Everest, and T. Ward
10 The Elementary Proof of the Prime Number Theorem: An Historical Perspective	179	(14)
D. Goldfeld
11 Additive Bases Representations and the Erdös-Turán Conjecture	193	(8)
G. Grekos, L. Haddad, C. Helou, and J. Pikho
12 The Boundary Structure of the Sumset in Z2	201	(18)
Shu-Ping Sandie Han
13 On NTUs in Function Fields	219	(2)
Howard Kleiman
14 Continued Fractions and Quadratic Irrationals	221	(32)
Joseph Lewittes
15 The Inverse Problem for Representation Functions of Additive Bases	253	(10)
Melvyn B. Nathanson
16 On the Uniquity of Sidon Sets	263
Melvyn B. Nathanson