Mann's theorem, proved by Henry Mann in 1942, resolved a long-standing question about Schnirelmann density known as the alpha plus beta hypothesis, previously used without proof by Edmund Landau. It states that for two sets of natural numbers A and B, the Schnirelmann density of their sumset is at least the sum of their individual Schnirelmann densities, even when the sumset falls short of covering all natural numbers. The theorem underpins the use of Schnirelmann density, a density measure developed by Lev Schnirelmann, in additive number theory problems including Waring's problem and Goldbach's conjecture.
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Source Schnirelmann density (Wikipedia)
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Source Henry Mann (Wikipedia)
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1. Mann's theorem (Wikipedia)
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In additive number theory, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is.
2. Schnirelmann density (Wikipedia)
- It was used by Edmund Landau and was finally proved by Henry Mann in 1942
In Branch: Number Theory, Lead sentence
In additive number theory, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is.
View the SourceHenry Mann (Wikipedia)
Principal Result Of: Henry Mann, Early life, Mann's theoremQuote, Principal Result Of: Henry Mann, Early life, Mann's theorem
By doing so he established Mann's theorem
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