527 research outputs found
Hecke grids and congruences for weakly holomorphic modular forms
Let denote the Atkin operator of prime index . Honda and Kaneko
proved infinite families of congruences of the form
for weakly holomorphic modular forms of low weight and level and primes in
certain residue classes, and conjectured the existence of similar congruences
modulo higher powers of . Partial results on some of these conjectures were
proved recently by Guerzhoy. We construct infinite families of weakly
holomorphic modular forms on the Fricke groups for
and describe explicitly the action of the Hecke algebra on these forms. As a
corollary, we obtain strengthened versions of all of the congruences
conjectured by Honda and Kaneko
Mock theta functions and weakly holomorphic modular forms modulo 2 and 3
We prove that the coefficients of certain mock theta functions possess no
linear congruences modulo 3. We prove similar results for the moduli 2 and 3
for a wide class of weakly holomorphic modular forms and discuss applications.
This extends work of Radu on the behavior of the ordinary partition function
modulo 2 and 3.Comment: 19 page
Euler-like recurrences for smallest parts functions
We obtain recurrences for smallest parts functions which resemble Euler's
recurrence for the ordinary partition function. The proofs involve the
holomorphic projection of non-holomorphic modular forms of weight 2
Congruences for modular forms of weights two and four
AbstractWe prove a conjecture of Calegari and Stein regarding mod p congruences between modular forms of weight four and the derivatives of modular forms of weight two
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