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arXiv · 2510.04873

Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums

Danylo Radchenko·Qihang Sun
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Abstract

We give a construction of radial Fourier interpolation formulas in dimensions 3 and 4 using Maass--Poincar\'e type series. As a corollary we obtain explicit formulas for the basis functions of these interpolation formulas in terms of what we call real-variable Kloosterman sums, which were previously introduced by Stoller. We also improve the bounds on the corresponding basis functions $a_{n,d}(x)$, $d=3,4$, for fixed $x$, in terms of the index $n$.

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Danylo Radchenko, Qihang Sun. 2025-10-06. Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums. https://arxiv.org/abs/2510.04873

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