Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coe‰cients of a modular form of weight 3=2… (More)

We prove that the coefficients of certain weight −1/2 harmonic Maass forms are “traces” of singular moduli for weak Maass forms. To prove this theorem, we construct a theta lift from spaces of weight… (More)

We investigate the arithmetic and combinatorial significance of the values of the polynomials jn(x) defined by the q-expansion ∞ ∑ n=0 jn(x)q := E4(z)E6(z) ∆(z) · 1 j(z) − x They allow us to provide… (More)

1. Introduction. Let k be an integer and N be a positive integer divisible by 4. If is a prime, denote by v a continuation of the usual-adic valuation on Q to a fixed algebraic closure. Let f be a… (More)

Recent works, mostly related to Ramanujan’s mock theta functions, make use of the fact that harmonic weak Maass forms can be combinatorial generating functions. Generalizing works of Waldspurger,… (More)

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight… (More)

Harmonic weak Maass forms of half-integral weight are the subject of many recent works. They are closely related to Ramanujan's mock theta functions, their theta lifts give rise to Arakelov Green… (More)

In the present paper we find explicit formulas for the degrees of Heegner divisors on arithmetic quotients of the orthogonal group O(2, p) and for the integrals of certain automorphic Green’s… (More)