Harmonic analysis in weighted -spaces
Hecke eigenforms in the cohomology of congruence subgroups of .
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.
Higher order invariants in the case of compact quotients
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case, many things simplify and we are thus able to prove a more precise structure theorem than in the general case.