In mathematics, a Kloosterman sum is a particular kind of exponential sum. They are named for the Dutch mathematician Hendrik Kloosterman, who introduced them in 1926[1] when he adapted the Hardy–Littlewood circle method to tackle a problem involving positive definite diagonal quadratic forms in four as opposed to five or more variables, which [vague] he had dealt with in his dissertation in 1924.[2]
Let a, b, m be natural numbers. Then
Here x* is the inverse of x modulo m.
^Kloosterman, H. D. On the representation of numbers in the formax2 + by2 + cz2 + dt2, Acta Mathematica 49 (1926), pp. 407–464
^Kloosterman, H. D. Over het splitsen van geheele positieve getallen in een some van kwadraten, Thesis (1924) Universiteit Leiden
mathematics, a Kloostermansum is a particular kind of exponential sum. They are named for the Dutch mathematician Hendrik Kloosterman, who introduced...
and ζ = e 2 π i q {\displaystyle \zeta =e^{\frac {2\pi i}{q}}} the Kloostermansum K ( a , b , χ ) {\displaystyle K(a,b,\chi )} is defined as K ( a ,...
"Analogues of Kloostermanssums". Izv. Ross. Akad. Nauk, Ser. Math. 59 (5): 93–102. Karatsuba, A. A. (1997). "Analogues of incomplete Kloostermansums and their...
calculate certain zeta functions. Quadratic Gauss sum Elliptic Gauss sum Jacobi sum Kummer sumKloostermansum Gaussian period Hasse–Davenport relation Chowla–Mordell...
Kloosterman is a Dutch surname. Notable people with the surname include: Hendrik Kloosterman (1900–1968), Dutch mathematician Kloostermansum Karin Kloosterman...
restricted by some inequality. Examples of complete exponential sums are Gauss sums and Kloostermansums; these are in some sense finite field or finite ring analogues...
multiplicative inverse figures prominently in the definition of the Kloostermansum. Inversive congruential generator – a pseudo-random number generator...
Douwe Kloosterman (9 April 1900 – 6 May 1968) was a Dutch mathematician, known for his work in number theory (in particular, for introducing Kloosterman sums)...
Petersson trace formula. The Kuznetsov or relative trace formula connects Kloostermansums at a deep level with the spectral theory of automorphic forms. Originally...
higher order derivatives of the zeta function and their associated Kloostermansums. Most zeros lie close to the critical line. More precisely, Bohr &...
trigonometric sums (Gauss sums) with algebro-geometric methods. He introduced the Katz–Lang finiteness theorem. Gauss sums, Kloostermansums, and monodromy...
\delta } is the Kronecker delta function, S {\displaystyle S} is the Kloostermansum and J {\displaystyle J} is the Bessel function of the first kind. Henryk...
Christelle (2015). "Galois representations attached to moments of Kloostermansums and conjectures of Evans". Compositio Mathematica. 151 (1): 68–120...
providing network participants better results from relevant efforts. Robert Kloosterman and Bart Lambregts define polycentric urban regions as collections of...
described in the paper Keshavarz, Raney & Campbell (1993) and in the paper Kloosterman & De Graaff (1989): the latter is a description of the Mextram[1] model...
Global Information