Vinogradov's Mean-Value Theorem is an estimate in analytic number theory bounding the number of solutions to a system of equations expressing equal sums of powers of natural numbers. Named for I. M. Vinogradov, it is one of the fundamental inequalities of the subject, underlying his method for estimating exponential sums, and a fully sharp form of the estimate was eventually established using the modern technique of decoupling.
Facts
StatementVinogradov's mean value theorem gives an upper bound on the number of solutions of a system of equations expressing equal sums of powers of natural numbers. 1 Classification
Statement Form Sources
1. Vinogradov's mean value theorem (Wikipedia)
Lead paragraph
In mathematics, Vinogradov's mean value theorem is an estimate for the number of equal sums of powers.
Introduction, historical note on Vinogradov's original bound
Vinogradov's original theorem of 1935 showed that for fixed s, k
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