Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations. More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Wemer in vector bundles on curves over

Provides a collection of more than 200 mathematical problems and their detailed solutions, which contain useful tips and skills in real analysis. This book is useful for undergraduate students during or after courses in calculus and linear algebra. It is also useful for graduate students who are interested in analytic number theory.

Provides a collection of more than 200 mathematical problems and their solutions, which contain useful tips and skills in real analysis. This book is suitable for undergraduate students during or after courses in calculus and linear algebra. It is also useful for graduate students who are interested in analytic number theory.

Covers many topics including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. This book contains many theoretical and applicated results in areas, such as: Serre's questions, answering a question in his letter to Top; and cryptographic applications of the discrete logarithm problem.

In the late 1970s, using higher algebraic K-theory, class field theory was generalized to higher-dimensional local and global fields. Thus, it is a very natural question to ask and seek, although conjectural in nature, for the higher-dimensional version of the reciprocity principle of Langlands and, more generally, the higher-dimensional analog of the functoriality principle of Langlands. However, there are very few works addressing this very important, open and exciting problem of current mathematics. This book aims at providing an introductory, detailed and up-to-date study of Kapranov's...

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory.Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory — quantitative theory of some surfaces and Bruedern et al's paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms — Kohnen's paper describes generalized modular forms (GMF)...

This volume is based on the successful 6th China-Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory — additive problems, divisor problems, Diophantine equations — to elliptic curves and automorphic L-functions. It contains new developments in number theory and the topics complement the existing two volumes from the previous seminars which can be found in the same...

This unique volume presents a fruitful and beautiful mathematical world hidden in Caianiello's neuronic equations, which describe the instantaneous behavior of a model of a brain or thinking machine. The detailed analysis from a viewpoint of “dynamical systems”, even in a single neuron case, enables us to obtain amazingly good rational approximations to the Hecke-Mahler series with two variables. Some interesting numerical applications of our rational approximations are also discussed.This book is fundamentally self-contained and many topics required in it are explained...

Based on the successful 7th China-Japan seminar on number theory conducted in Kyushu University, this volume is a compilation of survey and semi-survey type of papers by the participants of the seminar. The topics covered range from traditional analytic number theory to elliptic curves and universality. This volume contains new developments in the field of number theory from recent years and it provides suitable problems for possible new research at a level which is not unattainable. Timely surveys will be beneficial to a new generation of researchers as a source of information and these...