current version (1.31)
This is an introduction to the
arithmetic theory of modular functions and modular forms, with a greater
emphasis on the geometry than most accounts.
- Elliptic modular curves as Riemann surfaces
- Elliptic functions
- Modular functions and modular forms
- Hecke operators
- The modular equation for Gamma_0(N)
- The canonical model of X_0(N) over Q
- Modular curves as moduli varieties
- Modular forms, Dirichlet series, and functional equations
- Correspondences on curves; the theorem of Eichler and Shimura
- Curves and their zeta functions
- Complex multiplication for elliptic curves
The algebra and complex analysis usually covered in advanced undergraduate or
first-year graduate courses.
v1.10; May 22, 1997; first version on the web; 128 pages.
old version (1.10)
v1.20; November 23, 2009; new style; minor fixes and improvements; addedlist of symbols; 129 pages.
v1.30; April 26, 2012; corrected; many minor revisions; 138 pages.
v1.31; March 22, 2017; corrected; minor revisions; 134 pages.