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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]
The title of his thesis was "Evaluation of certain character sums". [1] He was a Putnam Fellow at MIT in 1970. [2] He received his Ph.D. in Mathematics from MIT for his thesis "The 4-part of the class group of a quadratic field", in 1974. [1] [3] His advisor for both his masters and Ph.D was Harold Stark. [1]
Brauer's theorem on induced characters (representation theory of finite groups) Brauer's three main theorems (finite groups) Brauer–Cartan–Hua theorem (ring theory) Bregman–Minc inequality (discrete mathematics) Brianchon's theorem ; British flag theorem (Euclidean geometry) Brooks's theorem (graph theory) Brouwer fixed-point theorem
In mathematics, Ramanujan's master theorem, named after Srinivasa Ramanujan, [1] is a technique that provides an analytic expression for the Mellin transform of an analytic function. Page from Ramanujan's notebook stating his Master theorem.
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 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.
“Blue Bloods” is saying goodbye to two special men: Treat Williams and his character, Lenny Ross. The former partner of New York Police Commissioner Francis “Frank” Reagan, played by Tom ...
Portrayed by Nick Gehlfuss. Dr. William "Will" Halstead is an attending in the Emergency Department. [1] He was first introduced to the Chicago franchise in the Chicago P.D. episode "Say Her Real Name" as Detective Jay Halstead's estranged brother who drops by to visit in a two-episode arc.