The 13 chapters of this book centre around the proof ofTheorem 1 of Faltings' paper "Diophantine approximation onabelian varieties," Ann. Math.133 (1991) and together givean approach to the proof that is accessible to Ph.D-levelstudents in number theory and algebraic geometry. Eachchapter is based on an instructional lecture given by itsauthor ata special conference for graduate students, on thetopic of Faltings' paper.
The 13 chapters of this book centre around the proof ofTheorem 1 of Faltings' paper "Diophantine approximation onabelian varieties," Ann. Math.133 (19...
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level...
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. ...
