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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).
In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the values of the complex exponential function with coefficients given by a quadratic character; for a general character, one obtains a more general Gauss sum.
In mathematics, the Gross–Koblitz formula, introduced by Gross and Koblitz expresses a Gauss sum using a product of values of the p-adic gamma function. It is an analog of the Chowla–Selberg formula for the usual gamma function. It implies the Hasse–Davenport relation and generalizes the Stickelberger theorem.
HCMUSSH was formerly known as the College of Letters, University of Saigon (Vietnamese: Trường Đại học Văn khoa, Viện Đại học Sài Gòn). It is now the biggest research and training center in the field of social sciences and humanities in Southern Vietnam. In October 2021, HCMUSSH officially claimed their autonomy in the ...
Given an integer n > 1, let H be any subgroup of the multiplicative group = (/) of invertible residues modulo n, and let = (). A Gaussian period P is a sum of the primitive n-th roots of unity , where runs through all of the elements in a fixed coset of H in G.
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.
In October 1945, President Hồ Chí Minh signed the decree to establish the University of Literature (Ban Đại học Văn khoa, or Trường Đại học Văn khoa) -the precursor of the current VNU-USSH. In April 1956, the University of Hanoi (Trường Đại học Tổng hợp Hà Nội) was established. During this period, fundamental ...
Map of ancient Asia shows location of the Âu Việt state of Nam Cương and other Viet’s kingdoms. According to folklore, prior to Chinese domination of northern and north-central Vietnam, the region was ruled by a series of kingdoms called Văn Lang with a hierarchical government, headed by Lạc Kings ( Hùng Kings ), who were served by ...