Abstract. For 2 < k ∈ 1 2 Z, we define lifts of cuspidal Poincaré series in Sk(Γ0(N)) to weight 2 − k harmonic weak Maass forms. This construction answers a question of Dyson by providing the general framework “explaining” Ramanujan’s mock theta functions. As an application, we show that the number of partitions of a positive integer n is the “trace” of singular moduli of a Maass form arising f...

discussion while this novel type of drug delivery is known as a suitable substitute for oral and parenteral administration, it was well accepted and extensively mentioned in persian medical and pharmaceutical manuscripts and other traditional systems of medicine as well. accordingly, medieval pharmaceutical standpoints on nasal dosage forms could still be an interesting subject of study. theref...

We introduce Galois families of modular forms. They are a new kind family coming from representations the absolute groups rational function fields over ℚ. exhibit some examples and provide an infinite non-liftable weight one Katz eigenforms $$\overline {{\mathbb{F}_p}}$$ for p ∈ {3, 5, 7, 11}.