Mock Heegner Points and Congruent Numbers.
Mock modular forms and singular combinatorial series
A celebrated result of Bringmann and Ono shows that the combinatorial rank generating function exhibits automorphic properties after being completed by the addition of a non-holomorphic integral. Since then, automorphic properties of various related combinatorial families have been studied. Here, extending work of Andrews and Bringmann, we study general infinite families of combinatorial q-series pertaining to k-marked Durfee symbols, in which we allow additional singularities. We show that these...
Mod p Hecke Operators and Congruences Between Modular Forms.
Modular Curves and the Class Group of Q(...p).
Modular curves and the Eisenstein ideal
Modular curves of composite level
Modular Decent and the Saito-Kurokawa Conjecture.
Modular embeddings and rigidity for Fuchsian groups
We prove a rigidity theorem for semiarithmetic Fuchsian groups: If Γ₁, Γ₂ are two semiarithmetic lattices in PSL(2,ℝ ) virtually admitting modular embeddings, and f: Γ₁ → Γ₂ is a group isomorphism that respects the notion of congruence subgroups, then f is induced by an inner automorphism of PGL(2,ℝ ).
Modular equations of hyperelliptic X₀(N) and an application
Modular forms and class number congruences
Modular forms and de Rham cohomology; Atkin-Swinnerton-Dyer congruences.
Modular forms and Galois Representations
Modular Forms and Root Systems.
Modular Forms Associated to Real Quadratic Fields.
Modular forms for Fr [T].
Modular forms of genus 2 and weight 1.
Modular Forms of Half Integral Weight, Some Explicit Arithmetic.
Modular Forms of Half-Integral Weight on ...0(4).
Modular Forms of Varying Weight. I.
Modular Forms of Varying Weight. II.