4 papers · 1 filter
Transformation of Third Order Mock Theta Functions and New -Series Identities
Frank Garvan, Avi Mukhopadhyay
Ramanujan introduced mock theta functions in his last letter to G.H.Hardy. He provided examples and various relations between them. G.N.Watson found transformations for the third o…
An infinite family of overpartition congruences mod powers of 2
Zhumagali Shomanov, Frank Garvan
We prove an infinite family of Hecke-like congruences for the overpartition function modulo powers of 2. Starting from a recent identity of Garvan and Morrow and iterating Atkin's…
Multiplicative congruences for Andrews's even parts below odd parts function and related infinite products
Frank Garvan, Connor Morrow
We prove multiplicative congruences mod for George Andrews's partition function, , the number of partitions of in which every even part is…
A simple proof of the Atkin-O'Brien partition congruence conjecture for powers of 13
Frank Garvan, Zhumagali Shomanov
In 1967, Atkin and O'Brien conjectured congruences for the partition function involving Hecke operators modulo powers of 13. In this paper, we provide a simple proof of this conjec…