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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]
In mathematics, a character sum is a sum () of values of a Dirichlet character χ modulo N, taken over a given range of values of n.Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue modulo N.
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 ...
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.
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 master theorem; Ramanujan's sum; Ramanujan's ternary quadratic form; Rank of a partition; Rogers–Ramanujan ...
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The Deccan Chronicle called Ramanujan "a brilliant piece on canvas with edifying moments and relevance to modern age" and went on to add that it was "not to be missed", giving it 3.5/5 stars. [19] S. Saraswathi of Rediff wrote, "Ramanujan is a brilliant film, a must watch" and gave the film 4/5. [20]
Ramanujan (name), a Tamil and Malayalam name; Srinivasa Ramanujan (1887–1920) was an Indian mathematician; A. K. Ramanujan was an Indian poet and scholar; Amita Ramanujan is a fictional character from the CBS crime drama Numb3rs; Ramanujan Hegde is a group leader at the Medical Research Council (MRC)