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About: Vinogradov's mean-value theorem     Goto   Sponge   NotDistinct   Permalink

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In mathematics, Vinogradov's mean value theorem is an estimate for the number of equal sums of powers.It is an important inequality in analytic number theory, named for I. M. Vinogradov. More specifically, let count the number of solutions to the system of simultaneous Diophantine equations in variables given by with . That is, it counts the number of equal sums of powers with equal numbers of terms and equal exponents,up to th powers and up to powers of . An alternative analytic expression for is where Vinogradov's mean-value theorem gives an upper bound on the value of .