6 papers
Definability via the tilting correspondence
Gessica Alecci, Ihsane Hadeg, Franziska Jahnke +2
We show that arithmetic definability of henselian valuations is preserved by the tilting correspondence. Moreover, we show that if a perfectoid valuation is arithmetically definabl…
A Shintani lift for rigid cocycles
Isabella Negrini
We construct a Shintani lift for rigid analytic cocycles of higher weight, attaching modular forms of half-integral weight to such cocycles. The expression for the Fourier coeffici…
The quaternionic Maass Spezialschar on split
Jennifer Johnson-Leung, Finn McGlade, Isabella Negrini +2
The classical Maass Spezialschar is a Hecke-stable subspace of the space of holomorphic Siegel modular forms of genus two and level one cut out by certain linear relations among Fo…
A Shimura-Shintani correspondence for rigid analytic cocycles of higher weight
Isabella Negrini
This paper takes the first steps towards a systematic study of additive rigid meromorphic cocycles of higher weight. These were introduced by Darmon and Vonk, who focused on multip…
Mock theta functions and related combinatorics
Cristina Ballantine, Hannah E. Burson, Amanda Folsom +3
In this paper we add to the literature on the combinatorial nature of the mock theta functions, a collection of curious -hypergeometric series introduced by Ramanujan in his las…
On a Partition Identity of Lehmer
Cristina Ballantine, Hannah E. Burson, Amanda Folsom +3
Euler's identity equates the number of partitions of any non-negative integer n into odd parts and the number of partitions of n into distinct parts. Beck conjectured and Andrews p…