5 papers
Exact formulae for ranks of partitions
Qihang Sun
In 2009, Bringmann arXiv:0708.0691 [math.NT] used the circle method to prove an asymptotic formula for the Fourier coefficients of rank generating functions. In this paper, we prov…
The basis functions of Fourier interpolation
David Berghaus, Andriy Bondarenko, Danylo Radchenko +2
The basis functions of the Fourier interpolation formula of Radchenko and Viazovska, constructed by means of weakly holomorphic modular forms for the Hecke theta group, are entire…
Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums
Danylo Radchenko, Qihang Sun
We give a construction of radial Fourier interpolation formulas in dimensions 3 and 4 using Maass--Poincaré type series. As a corollary we obtain explicit formulas for the basis f…
Uniform bounds for Kloosterman sums of half-integral weight, same-sign case
Qihang Sun
In the previous paper [Sun23], the author proved a uniform bound for sums of half-integral weight Kloosterman sums. This bound was applied to prove an exact formula for partitions…
Vanishing properties of Kloosterman sums and Dyson's conjectures
Qihang Sun
In a previous paper arXiv:2406.06294 [math.NT], the author proved the exact formulae for ranks of partitions modulo each prime . In this paper, for and , we prove…