Dynamics And Analytic Number Theory
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Dynamics and Analytic Number Theory
Author: Dzmitry Badziahin
language: en
Publisher: Cambridge University Press
Release Date: 2016-11-10
Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.
Analytic Number Theory: An Introductory Course
Author: Paul Trevier Bateman
language: en
Publisher: World Scientific
Release Date: 2004-09-07
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (”elementary”) and complex variable (”analytic”) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at www.math.uiuc.edu/~diamond/.
Advanced Topics in the Arithmetic of Elliptic Curves
Author: Joseph H. Silverman
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-12-01
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.