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Srinivasa Ramanujan mentioned the sums in a 1918 paper. [1] In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently large odd number is the sum of three primes. [2]
Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series.Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties that make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.
Srinivasa Ramanujan Aiyangar [a] (22 December 1887 – 26 April 1920) was an Indian mathematician.Often regarded as one of the greatest mathematicians of all time, though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then ...
The Ramanujan Journal; Ramanujan Math Park; Ramanujan Mathematical Society; Ramanujan prime; Ramanujan summation; Ramanujan tau function; Ramanujan theta function; Ramanujan–Nagell equation; Ramanujan–Petersson conjecture; Ramanujan–Sato series; Ramanujan–Soldner constant; Ramanujan's congruences; Ramanujan's lost notebook; Ramanujan's ...
The initial idea is usually attributed to the work of Hardy with Srinivasa Ramanujan a few years earlier, in 1916 and 1917, on the asymptotics of the partition function.It was taken up by many other researchers, including Harold Davenport and I. M. Vinogradov, who modified the formulation slightly (moving from complex analysis to exponential sums), without changing the broad lines.
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Zhang in Berkeley in 2021. Ruixiang Zhang is a mathematician specializing in Euclidean harmonic analysis, analytic number theory, geometry and additive combinatorics.He is an assistant professor in the Department of Mathematics at University of California, Berkeley. [1]
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