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The case originally considered by Carl Friedrich Gauss was the quadratic Gauss sum, for R the field of residues modulo a prime number p, and χ the Legendre symbol.In this case Gauss proved that G(χ) = p 1 ⁄ 2 or ip 1 ⁄ 2 for p congruent to 1 or 3 modulo 4 respectively (the quadratic Gauss sum can also be evaluated by Fourier analysis as well as by contour integration).
The generalized quadratic Gauss sum G(a, b, c) is defined by G ( a , b , c ) = ∑ n = 0 c − 1 e 2 π i a n 2 + b n c {\displaystyle G(a,b,c)=\sum _{n=0}^{c-1}e^{2\pi i{\frac {an^{2}+bn}{c}}}} . The classical quadratic Gauss sum is the sum g ( a , p ) = G ( a , 0, p ) .
This is an accepted version of this page This is the latest accepted revision, reviewed on 14 February 2025. German mathematician, astronomer, geodesist, and physicist (1777–1855) "Gauss" redirects here. For other uses, see Gauss (disambiguation). Carl Friedrich Gauss Portrait by Christian Albrecht Jensen, 1840 (copy from Gottlieb Biermann, 1887) Born Johann Carl Friedrich Gauss (1777-04-30 ...
This album contains 9 tracks in Vietnamese and 1 track in English, including the songs: "Đã Qua Thời Mong Chờ" (one of the notable songs of Vietnamese overseas music in the late 1990s, written by Trúc Hồ and Trầm Tử Thiêng [5] [6] [7]), "Hà Nội Mùa Vắng Những Cơn Mưa", [8] [9] "Đi Về Nơi Xa" [10] (two famous songs of Vietnamese music in the late 1990s), "Làm Sao ...
Tuấn Ngọc was born in Da Lat, Vietnam; in an artistic-traditioned family.His siblings are all well-known singers in Vietnam during the 1990s, including singer Khánh Hà (1952).
In mathematics, an elliptic Gauss sum is an analog of a Gauss sum depending on an elliptic curve with complex multiplication. The quadratic residue symbol in a Gauss sum is replaced by a higher residue symbol such as a cubic or quartic residue symbol, and the exponential function in a Gauss sum is replaced by an elliptic function.
A summation method that is linear and stable cannot sum the series 1 + 2 + 3 + ⋯ to any finite value. (Stable means that adding a term at the beginning of the series increases the sum by the value of the added term.) This can be seen as follows. If + + + =, then adding 0 to both sides gives
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