If p is prime, then let φp denote the Legendre symbol modulo p and let p be the trivial character modulo p. As usual, let n+1Fn(x)p := n+1Fn „ φp, φp, . . . , φp p, . . . , p | x « p be the Gaussian… Expand

It is reported that such congruences are much more widespread than was previously known, and the theoretical framework that appears to explain every known Ramanujan-type congruence is described.Expand

Let p(n) denote the number of partitions of the positive integer n; p(n) is the number of representations of n as a non-increasing sequence of positive integers (by convention, we agree that p(0) = 1… Expand

seem to be distinguished by the fact that they are exceptionally rare. Recently, Ono [O1] has gone some way towards quantifying the latter assertion. More recently, Ono [O2] has made great progress… Expand

We investigate divisibility properties of the traces and Hecke traces of singular moduli. In particular we prove that, if p is prime, these traces satisfy many congruences modulo powers of p which… Expand

We study the Gaussian hypergeometric series of type 3 F 2 over finite fields F p . For each prime p and each λ ∈ F p , we explicitly determine p 2 3 F 2(λ) p (mod p 2). Using this perspective, we are… Expand

This operator plays a fundamental role in the theory of modular forms, modular forms modulo p, and p-adic modular forms (see, for example, [Se], [Sw-D]). In a recent paper [B-K-O], Bruinier, Kohnen,… Expand