I'm interested in learning about partitions and modular forms. I already know algebra and analysis (complex and real). Can any one suggest me books or other materials from where I can learn these materials.
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Have you looked at this paper?. Full reference:
Scott Ahlgren and Ken Ono, Addition and counting: the arithmetic of partitions, Notices Amer. Math. Soc. 48 (2001), no. 9, 978–984. MR 1854533 (2002e:11136)
It and the references therein might contain what you are looking for.
I'd like a good answer to this question too. It seems to be difficult to find a book that treats this at any length. There are very very many nice books on modular forms (e.g. Koblitz) but most seem to just mention the partition function as an application, in passing. From the table of contents, Farkas and Kra "Theta constants, Riemann surfaces, and the modular group", seems promising. There is also Apostol "Modular Functions and Dirichlet Series...", which will certainly be more accessible.
For partitions you cannot go wrong with George Andrews' book "The Theory of Partitions". I am sure he mentions modular forms in it, but I do not recall that he goes into much detail about them. He has a second book (with Eriksson) on partitions that is very nice.