answers a natural question after Dirichlet's theorem on arithmetic progressions. It asserts that there exist positive c and L such that, if we denote p(a,d)...

for the L-function of some imaginary quadratic Dirichlet character then h(D) → ∞ as D → −∞. (In the work of Hecke and Heilbronn, the only L-functions...

transformées de Fourier. Applications. Mathematical Society of Japan. Mandelbrojt, Szolem (1972) [1969]. Dirichlet series. Principles and methods [Séries de Dirichlet...

Kolmogorov, "Une série de Fourier–Lebesgue divergente presque partout", Fundamenta Mathematicae 4 (1923), 324–328. Andrey Kolmogorov, "Une série de Fourier–Lebesgue...

also arises as the Euler-Lagrange equation of a functional called the Dirichlet energy. As such, the theory of harmonic maps contains both the theory...

zeta function and the Dirichlet L-function satisfy the Euler product, and due to their completely multiplicative property Are there L-functions other than...

for the associated Dirichlet form operator. This result means that if a function is in the range of the exponential of the Dirichlet form operator—which...

L2 function converges to it in L2 norm. After Dirichlet's result, several experts, including Dirichlet, Riemann, Weierstrass and Dedekind, stated their...

odd-exponent counterparts. Dirichlet's proof for n = 14 was published in 1832, before Lamé's 1839 proof for n = 7. Freeman L. "Fermat's One Proof". Retrieved...

a mixed boundary value problem, the solution is required to satisfy a Dirichlet or a Neumann boundary condition in a mutually exclusive way on disjoint...

polylogarithm function is defined by a power series in z, which is also a Dirichlet series in s: Li s ⁡ ( z ) = ∑ k = 1 ∞ z k k s = z + z 2 2 s + z 3 3 s...

(5): 279–281. doi:10.2307/3029800. JSTOR 3029800. Dirichlet PGL (1832). "Démonstration du théorème de Fermat pour le cas des 14e puissances". Journal für...

sum of convergent positive series" (PDF). Publications de l'Institut Mathématique. Nouvelle Série. 111 (125): 41–53. doi:10.2298/PIM2225041A. S2CID 237499616...

Mathematical Society. ISBN 978-0-8218-3573-9. Shimura, Goro (2007). Elementary Dirichlet Series and Modular Forms. Springer Monographs in Mathematics (Hardcover ed...

Gaetano Fichera in the paper (Fichera 1957), by using his solution of the Dirichlet problem for holomorphic functions of several variables and the related...

typical of physical processes, equality is customarily assumed, and the Dirichlet conditions provide sufficient conditions. The notation ∫ P {\displaystyle...

encyclopediaofmath.org. Retrieved 2024-07-16. "New Bounds for Large Values of Dirichlet Polynomials, Part 1 - Videos | Institute for Advanced Study". www.ias...

d'Augustin Cauchy. Série 1, tome 1 / publiées sous la direction scientifique de l'Académie des sciences et sous les auspices de M. le ministre de l'Instruction...

Courant, Richard (1977), Dirichlet's principle, conformal mapping, and minimal surfaces, Springer, ISBN 978-0-387-90246-3 Siegel, C. L. (1988), Topics in complex...

well-defined. The polynomials for M and N are easily related in terms of Dirichlet convolution of arithmetic functions f ( n ) ∗ g ( n ) {\displaystyle f(n)*g(n)}...

extent, the Dirichlet principle is valid under the hypothesis that Riemann was working with. However, in order to be valid, the Dirichlet principle needs...

based on the well known irrationality criterion from Peter Gustav Lejeune Dirichlet, which states that a number ξ {\displaystyle \xi } is irrational if there...

(PDF), Journal de mathématiques pures et appliquées, Série 1 (in French): 366–390. (Proof of the postulate: 371–382). Also see Mémoires de l'Académie Impériale...

OCLC 69616537. — (1909), "Sur l'unicité de la solution du problème de Dirichlet", Bulletin International de l'Académie des Sciences de Cracovie. Classe des Sciences...

"Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann", Journal de Mathématiques Pures et Appliquées, Neuvième Série, 63 (2): 187–213...

fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs", Comptes Rendus de l'Académie des Sciences, Série I, 331 (4):...

by Argand in 1806. Dirichlet's theorem on arithmetic progressions. In 1808 Legendre published an attempt at a proof of Dirichlet's theorem, but as Dupré...

applications to the subject of variational inequalities. By adapting the Dirichlet energy, it is standard to recognize solutions of certain wave equations...

Hadamard and de la Vallée Poussin, and the result is now known as the prime number theorem. Another important 19th century result was Dirichlet's theorem on...

boundary values that are continuous, but not analytic, as happens for Dirichlet's problem for the potential function . Hilbert stated his nineteenth problem...