Apr 6, 2016 · A modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying …

50 The theory of modular forms arose out of the study of elliptic integrals (as did the theory of elliptic curves, and much of modern algebraic geometry, and indeed much of modern mathematics).

Nov 10, 2021 · After watching all the 8 parts of "“Introduction to Modular Forms,” by Keith Conrad" on YouTube, I got "extremely intrigued" by plotting graphs of Modular Forms ( on SL (2,Z) ).

Dec 14, 2013 · 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 …

Modular forms can be seen as certain space of functions which provides you with concrete models of infinte dimensional representations of locally compact groups (SL (2,R) say). Modular forms can be …

Nov 8, 2022 · If I understand correctly, a weakly modular form is a "modular form" that could have poles. However, if the function is bounded in the neighborhood of a pole, then the singularity is removable …

Definition of a modular form in terms of differential forms Ask Question Asked 8 years ago Modified 8 years ago

Mar 11, 2025 · I am aware that this is a Jacobi form but I have seen in some papers that people will say that this is a modular form. My understanding is that $\Theta (-q^ {\frac {1} {2}};q)=\sum_nq^ {\frac …

Oct 16, 2023 · This is true for modular forms over $\Gamma_0 (N)$. There, the story is that the field of modular functions is given by $\mathbb {C} (j (z), j (Nz))$. But "all" modular forms is a potentially very …

Jul 29, 2024 · Use the "valence formula" (see here for statement and proof), relating a sum over the zeros of a (nonzero) modular form to the weight of the form. It follows easily from this that since …