# Course

## M560 - Modular Forms of One Variable

Course No:
M560
Credit:
4
Prerequisites:
M202 , M205, M207, M308
Approval:
2014
UG-Elective
Syllabus:
$SL_2 (\mathbb Z)$ and its congruence subgroups, Modular forms for $SL_2 (\mathbb Z)$, Modular forms for congruence subgroups, Modular forms and differential operators, Hecke theory, L-series, Theta functions and transformation formula.
Reference Books:
1. J.-P. Serre, “A Course in Arithmetic”, Graduate Texts in Mathematics 7, Springer- Verlag, 1973.
2. N. Koblitz, “Introduction to Elliptic Curves and Modular Forms”, Graduate Texts in Mathematics 97, Springer-Verlag, 1993.
3. J. H. Bruinier, G. van der Geer, G. Harder, D. Zagier, “The 1-2-3 of Modular Forms”, Universitext, Springer-Verlag, 2008.
4. F. Diamond, J. Shurman, “A First Course in Modular Forms”, Graduate Texts in Mathematics 228, Springer-Verlag, 2005.
5. S. Lang, “Introduction to Modular Forms”, Springer-Verlag, 1995.
6. G. Shimura, “Introduction to the Arithmetic Theory of Automorphic Forms”, Princeton University Press, 1994.