Illinois Journal of Mathematics

Improved estimates for the discrete Fourier restriction to the higher dimensional sphere

Jean Bourgain and Ciprian Demeter

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We improve the exponent in (Int. Math. Res. Not. IMRN 1993 (1993) 61–66) for the discrete restriction to the $n$ dimensional sphere, from $p=\frac{2(n+1)}{n-3}$ to $p=\frac{2n}{n-3}$, when $n\ge4$.

Article information

Illinois J. Math., Volume 57, Number 1 (2013), 213-227.

First available in Project Euclid: 23 June 2014

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Zentralblatt MATH identifier

Primary: 11L07: Estimates on exponential sums
Secondary: 11L05: Gauss and Kloosterman sums; generalizations 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30}


Bourgain, Jean; Demeter, Ciprian. Improved estimates for the discrete Fourier restriction to the higher dimensional sphere. Illinois J. Math. 57 (2013), no. 1, 213--227. doi:10.1215/ijm/1403534493.

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