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...

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

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...

_{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...

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...

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...