Number Theory

Tradition and Modernization

Wenpeng Zhang, Yoshio Tanigawa - Collection Developments in Mathematics

242 pages, parution le 26/03/2006

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Résumé

Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory. Though the topics and descriptive details appear varied, they are unified by two underlying principles: first, making everything readable as a book, and second, making a smooth transition from traditional approaches to modern ones by providing a rich array of examples.

The chapters are presented in quite different in depth and cover a variety of descriptive details, but the underlying editorial principle enables the reader to have a unified glimpse of the developments of number theory. Thus, on the one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated. The book emphasizes a few common features such as functional equations for various zeta-functions, modular forms, congruence conditions, exponential sums, and algorithmic aspects.

Sommaire

Preface
About the book and the conference
List of participants
Positive finiteness of number systems (S. Akiyama)
On a distribution property of the resudual order of a (mod p) -IV (K. Chinen and L. Murata)
Diagonalizing "bad" Hecke operators on spaces of cusp forms (Y.-J. Choie and W. Kohnen)
On the Hilbert-Kamke and the Vinogradov problems in additive number theory (V. N. Chubarikov)
The Goldbach-Vinogradov theorem in arithmetic progressions (Z. Cui)
Densities of sets of primes related to decimal expansion of rational numbers (T. Hadano, Y. Kitaoka, T. Kubota and M. Nozaki)
Spherical functions on p-adic homogeneous spaces (Y. Hironaka)
On modular forms of weight (6n + 1)=5 satisfying a certain differential equation (M. Kaneko)
Some aspects of the modular relation (S. Kanemitsu, Y. Tanigawa, H. Tsukada and M. Yoshimoto)
Zeros of automorphic L-functions and noncyclic base change (J. Liu and Y. Ye)
Analytic properties of multiple zeta-functions in several variables (K. Matsumoto)
Cubic fields and Mordell curves (K. Miyake)
Towards the reciprocity of quartic theta-Weyl sums, and beyond (Y.-N. Nakai)
Explicit congruences for Euler polynomials (Z.-W. Sun)
Square-free integers as sums of two squares (W. Zhai)
Some applications of L-functions to the mean value of the Dedekind sums and Cochrane sums (W. Zhang)
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Wenpeng Zhang, Yoshio Tanigawa
Collection	Developments in Mathematics
Parution	26/03/2006
Nb. de pages	242
Format	16 x 24
Couverture	Relié
Poids	367g
Intérieur	Noir et Blanc
EAN13	9780387304144
ISBN13	978-0-387-30414-4