293 citations · 357 across the 38 of their papers we have counts for
47 papers
Real quadratic fields and finite quantum dilogarithms I
Danylo Radchenko, Campbell Wheeler
We prove that Stark--Shintani ray class invariants (Stark units) associated to real quadratic fields are algebraic numbers. These invariants are given by special values of Faddeev'…
On Grünbaum's problem for symmetric configurations
Andrii Arman, Andriy Bondarenko, Andriy Prymak +1
Let be the largest number of Euclidean balls of diameter which may be needed to cover a set of diameter in . We study this problem for finite sets invar…
A construction of spherical -designs with points
Andrii Arman, Andriy Bondarenko, Andriy Prymak +1
For every we give an explicit equal-weight spherical -design in with at most points. Our approach utilizes recent construc…
An integrality phenomenon
Florian Fürnsinn, Danylo Radchenko, Wadim Zudilin
We prove a general statement about the integrality of the sequences generated by a recursion of the following form: equals a linear combination of $u_{n-1},u_{n-2},\dots,u_0…
On asymptotic Lebesgue's universal covering problem
Andrii Arman, Andriy Bondarenko, Andriy Prymak +1
A universal cover in is a measurable set that contains a congruent copy of any set of diameter 1. Lebesgue's universal covering problem, posed in 1914, asks for th…
Multiple polylogarithms and the Steinberg module
Steven Charlton, Danylo Radchenko, Daniil Rudenko
We establish a connection between multiple polylogarithms on a torus and the Steinberg module of , and show that multiple polylogarithms of depth and weight can…