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)...

} The Dirichlet hyperbola method re-expresses a sum of a multiplicative function f ( n ) {\displaystyle f(n)} by selecting a suitable Dirichlet convolution...

reciprocity law. The Dirichlet divisor problem, for which he found the first results by introducing the Dirichlet hyperbola method, is still an unsolved...

case the poset of positive integers ordered by divisibility. The Dirichlet hyperbola method computes the summation of a convolution in terms of its functions...

can be proven using the Dirichlet hyperbola method, and was first established by Dirichlet in 1849.: 37–38, 69  The Dirichlet divisor problem, precisely...

Dirichlet hyperbola method Dirichlet integral Dirichlet kernel (functional analysis, Fourier series) Dirichlet L-function Dirichlet principle Dirichlet problem...

Mangolt function. Estimate of the divisor summatory function of the Dirichlet hyperbola method. In some formulations of Zipf's law. The answer to the coupon...

_{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...

cycloid arch, Grégoire de Saint-Vincent investigated the area under a hyperbola (Opus Geometricum, 1647), and Alphonse Antonio de Sarasa, de Saint-Vincent's...

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...

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...

Adriaan van Roomen solved the problem using intersecting hyperbolas, but this solution uses methods not limited to straightedge and compass constructions...

from the harmonic numbers by a small constant, and Peter Gustav Lejeune Dirichlet showed more precisely that the average number of divisors is ln ⁡ n +...

{1}{x}}.} This problem can be phrased as quadrature of the rectangular hyperbola xy = 1. In 1647 Gregoire de Saint-Vincent noted that the required function...

series may fail the first part of the test. For a generalization, see Dirichlet's test. Leibniz discussed the criterion in his unpublished De quadratura...

_{1}^{x}{\frac {1}{t}}\,dt} representing the area between the rectangular hyperbola x y = 1 {\displaystyle xy=1} and the x-axis, was a logarithmic function...

Galois theory. 1832 – Lejeune Dirichlet proves Fermat's Last Theorem for n = 14. 1835 – Lejeune Dirichlet proves Dirichlet's theorem about prime numbers...

for x and y. In Cartesian coordinates, the equation is represented by a hyperbola; solutions occur wherever the curve passes through a point whose x and...

Investigation of a general Theorem for finding the Length of any Arc of any Conic Hyperbola, by Means of Two Elliptic Arcs, with some other new and useful Theorems...

results on local zeta-functions. Geometrically the sum is taken along a 'hyperbola' XY = ab and we consider this as defining an algebraic curve over the...

properties. Dirichlet's test Is a method of testing for the convergence of a series. It is named after its author Peter Gustav Lejeune Dirichlet, and was...

stretch the plane along one axis and squish it along the other, fixing hyperbolas of constant norm. The matrices ⁠ Φ 2 n + 1 {\displaystyle \mathbf {\Phi...