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Há 6 dias · The first sufficient conditions for the pointwise convergence of the Fourier series were discovered by a German mathematician Johann Peter Gustav Lejeune Dirichlet (1805--1859). A function that satisfies the Dirichlet conditions is also called piecewise monotone.
Há 6 dias · In 1838 Peter Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral li(x) (under the slightly different form of a series, which he communicated to Gauss).
23 de mai. de 2024 · Quadratic residue - Wikipedia. Contents. hide. (Top) History, conventions, and elementary facts. Prime modulus. Prime power modulus. Composite modulus not a prime power. Notations. Distribution of quadratic residues. Dirichlet's formulas. Law of quadratic reciprocity. Pairs of residues and nonresidues. The Pólya–Vinogradov inequality.
Há 5 dias · A conventional starting point for analytic number theory is Dirichlet's theorem on arithmetic progressions (1837), whose proof introduced L-functions and involved some asymptotic analysis and a limiting process on a real variable.
28 de mai. de 2024 · We provide an answer to a question raised by Levine and Weinberger in their 1986 paper concerning the difference between Dirichlet and Neumann eigenvalues of the Laplacian on bounded domains in $\R^ {n}$. More precisely, we show that for a certain class of domains there exists a sequence p(k) such that λk ≥ μk+p(k) for sufficiently large k.
Há 2 dias · Dirichlet's theorem is a theorem in number theory, which states that for any two coprime positive integers \(a\) and \(d\), there exists an infinite amount of positive integers \(n\) for which \(an + d \) is a prime number.
23 de mai. de 2024 · There are known two Dirichlet problems: either interior or inner Dirichlet problem or exterior or outer Dirichlet problem. The inner problem asks to find a solution of elliptic equation L[D]u = 0 inside the domain Ω given values on the boundary ∂Ω of Ω.
