Title: Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums Show Chinese title

Title: 三维和四维中的傅里叶插值以及实变量Kloosterman和

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 $n$. Show Chinese abstract

Abstract: 我们使用Maass--Poincaré型级数在三维和四维空间中构造了径向傅里叶插值公式。 作为推论，我们得到了这些插值公式的基函数的显式公式，这些公式涉及我们所谓的实变量Kloosterman和，这些和之前由Stoller引入。 我们还改进了对应基函数$a_{n,d}(x)$, $d=3,4$在固定$x$的情况下关于指标$n$的界限。