In number theory, the Dirichlet hyperbola method is a technique to evaluate the sum F ( n ) = ∑ k = 1 n f ( k ) , {\displaystyle F(n)=\sum _{k=1}^{n}f(k)...
5 KB (765 words) - 18:09, 19 October 2024
} The Dirichlet hyperbola method re-expresses a sum of a multiplicative function f ( n ) {\displaystyle f(n)} by selecting a suitable Dirichlet convolution...
40 KB (6,860 words) - 08:22, 14 October 2024
reciprocity law. The Dirichlet divisor problem, for which he found the first results by introducing the Dirichlet hyperbola method, is still an unsolved...
31 KB (3,581 words) - 02:30, 25 September 2024
Dirichlet hyperbola method Dirichlet integral Dirichlet kernel (functional analysis, Fourier series) Dirichlet L-function Dirichlet principle Dirichlet problem...
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case the poset of positive integers ordered by divisibility. The Dirichlet hyperbola method computes the summation of a convolution in terms of its functions...
16 KB (2,548 words) - 18:05, 14 October 2024
Divisor summatory function (redirect from Dirichlet divisor problem)
can be proven using the Dirichlet hyperbola method, and was first established by Dirichlet in 1849.: 37–38, 69 The Dirichlet divisor problem, precisely...
11 KB (1,936 words) - 16:54, 8 April 2024
Divisor sum identities (category Summability methods)
_{x=1}^{a}\sum _{y=1}^{b}g(x)h(y);} this is known as the Dirichlet hyperbola method. An arithmetic function is periodic (mod k), or k-periodic, if...
15 KB (2,878 words) - 17:09, 8 April 2024
cycloid arch, Grégoire de Saint-Vincent investigated the area under a hyperbola (Opus Geometricum, 1647), and Alphonse Antonio de Sarasa, de Saint-Vincent's...
22 KB (3,264 words) - 17:45, 24 October 2024
Integral (redirect from Methods of integration)
of a function, the hyperbolic logarithm, achieved by quadrature of the hyperbola in 1647. Further steps were made in the early 17th century by Barrow and...
69 KB (9,284 words) - 15:34, 27 October 2024
parabola, and the hyperbola the names by which we know them. Unknown (400 CE) It describes the archeo-astronomy theories, principles and methods of the ancient...
97 KB (10,409 words) - 10:05, 2 September 2024