26 citations · 37 across the 15 of their papers we have counts for
17 papers
The Shimura lift and congruences for modular forms with the eta multiplier
Scott Ahlgren, Nickolas Andersen, Robert Dicks
The Shimura correspondence is a fundamental tool in the study of half-integral weight modular forms. In this paper, we prove a Shimura-type correspondence for spaces of half-integr…
Congruences like Atkin's for the partition function
Scott Ahlgren, Patrick B. Allen, Shiang Tang
Let be the ordinary partition function. In the 1960s Atkin found a number of examples of congruences of the form where and are…
Scarcity of congruences for the partition function
Scott Ahlgren, Olivia Beckwith, Martin Raum
The arithmetic properties of the ordinary partition function have been the topic of intensive study for the past century. Ramanujan proved that there are linear congruences…
Dissections of strange -series
Scott Ahlgren, Byungchan Kim, Jeremy Lovejoy
In a study of congruences for the Fishburn numbers, Andrews and Sellers observed empirically that certain polynomials appearing in the dissections of the partial sums of the Kontse…
Maass forms and the mock theta function
Scott Ahlgren, Alexander Dunn
Let be the well-known third order mock theta of Ramanujan. In 1964, George Andrews proved an asymptotic formula of the form $$α(n)= \sum_{c\leq…
A polyharmonic Maass form of depth 3/2 for SL_2(Z)
Scott Ahlgren, Nickolas Andersen, Detchat Samart
Duke, Imamoglu, and Toth constructed a polyharmonic Maass form of level 4 whose Fourier coefficients encode real quadratic class numbers. A more general construction of such forms…