Description
Book SynopsisAn introductory survey of elliptic curves, modular forms, and $L$-functions. The main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory.
Trade Review...ambitious undergraduates need a chance to get to know the fabled cities, and now they have it. With any luck, they will fall in love with them and come help us explore their mysteries." -
MAA Reviews"A welcome addition to a serious mathematics library." - Michael Berg,
MAA Reviews"I think this is a wonderful book. In less than 200 pages Lozano-Robledo covers a solid amount of modern number theory in a manner altogether accessible to a novice, and in a fashion so as to convey number theory's irresistible beauty. . . . [T]he themes Lozano-Robledo addresses . . . are deep and sophisticated; considerable mathematical background is required for their mastery. But mastery is not what Lozano-Robledo is after: it's more along the lines of rendering 'the primary objects of study, the statements of the main theorems, and their corollaries . . . within the grasp of advanced undergraduates.' And in this objective Lozano-Robledo succeeds admirably. The book is full of examples and exercises of such appeal that a properly disposed rookie should go after nigh-on all of them; to boot, the author's narrative is compact and smooth.
Elliptic Curves, Modular Forms, and Their L-Functions is a marvelous addition to the literature. Had I had it available as a kid, it would have been among my very favorites!" -
CHOICE Reviews"The most remarkable aspect [of the book] is the emphasis on detailed analysis of the definitions and complete explanation of the statements of the main theorems and corollaries." - J. R. Delgado, European Mathematical Society
Table of Contents
- Preface
- Introduction
- Elliptic curves
- Modular curves
- Modular forms
- 𝐿-functions
- PARI/GP and Sage
- Complex analysis
- Projective space
- The 𝑝-adic numbers
- Parametrization of torsion structures
- Bibliography
- Index
