NOTES ON ATKIN–LEHNER THEORY FOR DRINFELD MODULAR FORMS

Math 847 Notes Modular Forms

Lecture Notes: An invitation to modular forms

1 Tate's thesis in the context of class field theory 1.1 Reciprocity laws Let K be a number field or function field. Let C K = A × K /K × be the idele class group. One of the main theorems of class field theory is the existence of a reciprocity map rec K : C K → Gal(K ab /K). This map is continuous with dense image. Whenever L/K is a finite abelian extension, there is a relative version of the ...

Eichler-shimura Theory for Mock Modular Forms

We use mock modular forms to compute generating functions for the critical values of modular L-functions, and we answer a generalized form of a question of Kohnen and Zagier by deriving the “extra relation” that is satisfied by even periods of weakly holomorphic cusp forms. To obtain these results we derive an Eichler-Shimura theory for weakly holomorphic modular forms and mock modular forms. T...

Analytic Theory of Modular Forms

The Poisson Kernel for Drinfeld Modular Curves

In an earlier work [T I], the author described a technique for constructing rigid analytic modular forms on the p-adic upper half plane by means of an integral transform (a "Poisson Kernel"). In this paper, we apply these methods to the study of rigid analytic modular forms on the upper half plane over a complete local field k of characteristic p. Arising out of the theory of Drinfeld modules [...