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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 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.
The Man Who Knew Infinity: A Life of the Genius Ramanujan is a biography of the Indian mathematician Srinivasa Ramanujan, written in 1991 by Robert Kanigel.The book gives a detailed account of his upbringing in India, his mathematical achievements and his mathematical collaboration with mathematician G. H. Hardy.
Ramanujan summation is a method to isolate the constant term in the Euler–Maclaurin formula for the partial sums of a series. For a function f , the classical Ramanujan sum of the series ∑ k = 1 ∞ f ( k ) {\displaystyle \textstyle \sum _{k=1}^{\infty }f(k)} is defined as
Ramachandra, K. (1969), Lectures on transcendental numbers, The Ramanujan Institute Lecture Notes, vol. 1, The Ramanujan Institute, Madras, MR 0260678 Ramachandra, K. (1995), On the mean-value and omega-theorems for the Riemann zeta-function, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 85, Published for the Tata Institute of Fundamental Research, Bombay ...
In the Tamil biographical film Ramanujan (2014), actor Sarath Babu played the character Diwan Bahadur R. Ramachandra Rao ICS. The movie itself was about Srinivasa Ramanujan, one of the greatest mathematicians. [2] [3]
On Metacritic, the Windows and Xbox Series X/S versions of Serial Cleaners received mixed reviews, [4] [5] and the PlayStation 5 version received positive reviews. [6] Although they said the missions can become a bit repetitive, Rock Paper Shotgun said it "makes murder-cleaning a fun task that rewards patience or chaos". [2]