Advanced Number Theory with Applications

Richard A. Mollin is a professor in the Department of Mathematics and Statistics at the University of Calgary. In the past twenty-three years, Dr. Mollin has founded the Canadian Number Theory Association and has been awarded six Killam Resident Fellowships. Over the past thirty-three years, he has written more than 190 publications.

The reader following this book will obtain a thorough overview of some very deep mathematics which is still in active research today. … I readily recommend this book to advanced undergraduates and beginning graduate students interested in advanced number theory. This book can also be read by the enthusiast who is well-acquainted with the author's previous book Fundamental Number Theory with Applications.—IACR Book Reviews, May 2011… each section comes with a large number of illustrating examples and accompanying exercises. … The rich bibliography contains 106 references, where maximum information is imparted by explicit page reference for each citing of a given item within the text. The carefully compiled index has more than 1,500 entries presented for maximum cross-referencing. Overall, this excellent textbook bespeaks the author’s outstanding expository mastery just as much as his mathematical erudition and elevated taste. Presenting a wide panorama of topics in advanced classical and contemporary number theory, and that in an utmost lucid and comprehensible style of writing, the author takes the reader to the forefront of research in the field, and on a truly exciting journey over and above.—Werner Kleinert, Zentralblatt MATH, 2010When I was looking over books for my course, I was very pleased by yours, and look forward to teaching from it. … after much thought I found that I liked yours best for its completeness, its problems, and for the way you weave current results and conjectures into the text. … Among other things that pleased me about your book, I’m so glad continued fractions come where they do. … a worthy book …—David Barth-Hart, Associate Head, School of Mathematical Sciences, Rochester Institute of Technology, New York, USAThis terrific book is testimony to Richard Mollin’s mathematical erudition, wonderful taste, and also his breadth of culture. … Mollin’s treatment of elliptic curves is a model of clear exposition … [It] succeeds very well in its goal of providing a means of transition from more or less foundational material to papers and advanced monographs, i.e., research in the field. … a wondrous book, successfully fulfilling the author’s purpose of effecting a bridge to modern number theory for the somewhat initiated. … it’s very nice to find in Mollin’s book a high quality and coherent treatment of this beautiful material and pointers in abundance to where to go next.—Michael Berg, Loyola Marymount University, MAA Review, 2009

• Algebraic Number Theory and Quadratic Fields. Ideals. Binary Quadratic Forms. Diophantine Approximation. Arithmetic Functions. Introduction to p-Adic Analysis. Dirichlet: Characters, Density, and Primes in Progression. Applications to Diophantine Equations. Elliptic Curves. Modular Forms. Appendix. Bibliography. Solutions to Odd-Numbered Exercises. Indices.