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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]
The Maryland Constitution of 1776 was the first of four constitutions under which the U.S. state of Maryland has been governed. It was that state's basic law from its adoption in 1776 until the Maryland Constitution of 1851 took effect on July 4 of that year.
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 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
Melony G. Griffith, Larry Hogan and Adrienne A. Jones enacting Maryland law in April 2022. The Annotated Code of Maryland, published by The Michie Company, is the official codification of the statutory laws of Maryland. It is organized into 36 named articles. The previous code, organized into numbered articles, has been repealed. [1]
Lewis W. Green (January 28, 1806 – May 26, 1863) was an American Presbyterian minister, educator, and academic administrator. Born in Danville, Kentucky, and educated in Woodford County, he enrolled at Transylvania University but transferred to Centre College to complete his degree.