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This document summarizes new methods for analyzing Fourier restriction problems. It introduces an efficient congruencing method to obtain bounds for periodic Strichartz inequalities and discrete Fourier restriction problems. For any complex sequence and when s > k(k+1), the method provides an upper bound for an integral involving exponential sums over the curve (n,n^2,...,n^k). This implies corresponding bounds for the constants in related inequalities, of the conjectured optimal order of magnitude.

Author

yazdanadzi

Language

EN