Hecke operators and Lambert series.
Hecke operators in half-integral weight
In [6], Shimura introduced modular forms of half-integral weight, their Hecke algebras and their relation to integral weight modular forms via the Shimura correspondence. For modular forms of integral weight, Sturm’s bounds give generators of the Hecke algebra as a module. We also have well-known recursion formulae for the operators with prime. It is the purpose of this paper to prove analogous results in the half-integral weight setting. We also give an explicit formula for how operators ...
Heegner cycles, modular forms and jacobi forms
We give a geometric interpretation of an arithmetic rule to generate explicit formulas for the Fourier coefficients of elliptic modular forms and their associated Jacobi forms. We discuss applications of these formulas and derive as an example a criterion similar to Tunnel's criterion for a number to be a congruent number.
Heegner points and derivatives of L-series.
Heights of Heegner points on Shimura curves.
Hida families, -adic heights, and derivatives
This paper concerns the arithmetic of certain -adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a -adic regulator, and the derivative of a -adic -function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first...
Higher order modular forms and mixed Hodge theory
Hodge-Tate Structures and Modular Forms.
Höhere Reziprozitätsgesetze und Modulformen vom Gewicht Eins.
How to compute the coefficients of the elliptic modular function .
Hyperbolic tessellations, modular symbols, and elliptic curves over complex quadratic fields
Hyperelliptic modular curves
Hyperelliptic modular curves X₀*(N) with square-free levels