be the standard theta function. Then θ which is the generating function for rs(n) (n ∈ N), is a modular form of weight s 2 and level 4 and hence for s ≥ 4 can be expressed as the sum of a modular… (More)

We use spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply… (More)

In this paper we construct certain mock modular forms of weight 1/2 whose Fourier coefficients are given in terms of cycle integrals of the modular j-function. Their shadows are weakly holomorphic… (More)

To an ideal class of a real quadratic field we associate a certain surface. This surface, which is a new geometric invariant, has the usual modular closed geodesic as its boundary. Furthermore, its… (More)

The existence of such a basis is well-known, and our aim here is to illustrate the effectiveness of using weakly holomorphic forms in providing one. Our main goal is to construct modular integrals… (More)

There are numerous connections between quadratic fields and modular forms. One of the most beautiful is provided by the theory of singular invariants, which are the values of the classical j-function… (More)

Hecke proved the meromorphic continuation of a Dirichlet series associated to the lattice points in a triangle with a real quadratic slope and found the possible poles in terms of the fundamental… (More)

It is known that the 3-manifold SL(2,Z)\ SL(2,R) is diffeomorhic to the complement of the trefoil knot in S3. As is shown by E. Ghys the linking number of the trefoil with a modular knot associated… (More)

It is known that the 3-manifold SL(2,Z)\ SL(2,R) is diffeomorphic to the complement of the trefoil knot in S. E. Ghys showed that the linking number of this trefoil knot with a modular knot is given… (More)