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math.NT2025
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…
math.NT2025
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 fu…
math.NT2023
Convolution identities for divisor sums and modular forms
Ksenia Fedosova, Kim Klinger-Logan, Danylo Radchenko
We prove exact identities for convolution sums of divisor functions of the form where $φ(…