Elliptic Curves, Modular Forms, and Their L-functions

The text grew out of lecture notes for a course Lozano-Robledo taught at an undergraduate summer school as part of the 2009 Park City Mathematics Institute. It is an introductory survey of the theory of elliptic curves, modular forms, and their Lfunctions, emphasizing examples rather than proofs. His goal is to provide a big picture of the surprising connections among these three types of mathematical objects, which seem so distinct. One theme is the statement of the modularity theorem (nee Taniyuama-Shimura-Weil conjecture), and one of its most renowned consequences, Fermat's last theorem. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)