I'm looking for an introductive book on Modular Forms and their applications to Algebraic Geometry and Algebraic Number Theory.
Some Ideas?
Explaining you my prerequisites, I've a good knowledge of basic instruments of Algebra and Algebraic Geometry, but I need some explanations in geometrical facts about Riemann Surfaces and Advanced Complex Analysis...
$\endgroup$4 Answers
$\begingroup$The first book you want to look at is Serre's "A course in arithmetic". THe second is the aptly named "A first course in modular forms"
$\endgroup$ 3 $\begingroup$Step $0$: J W Brown & R V Churchill - Complex Variables and Applications [→];
Step $\frac12$: E Freitag & R Busam : Complex Analysis [→];
Step $1$: E Freitag - Complex Analysis 2 [→].
$\endgroup$ $\begingroup$The book---"A first course in modular forms" by F. Diamond, J. Shurman is a good book to start to study classical modular forms. The advanced one--- "Modular forms" by Toshitsune Miyake is also a very good textbook to learn modular forms. Good luck.
$\endgroup$ 1 $\begingroup$Modular Forms A Classical Approach, by Henri Cohen and Fredrik Strömberg.
A recent book ( 2017 ) with lots of exercises, only prerequisite is complex analysis.
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