(number theory) Any infinite series of the form ∑ₙ₌₁ ᪲(a_n)/(nˢ), where s and each a_n are complex numbers.

plural of Dirichlet energy

(mathematical analysis, functional analysis, Fourier analysis) A quadratic functional which, given a real function defined on an open subset of ℝⁿ, yields a real number that is a measure of how variable said function is.

plural of Dirichlet character

(mathematics, mathematical analysis) The alternating sum of the Dirichlet series expansion of the Riemann zeta function: 𝜂(s)=∑ₙ₌₁ ᪲(-1)ⁿ⁻¹/nˢ=1/(1ˢ)-1/(2ˢ)+1/(3ˢ)-1/(4ˢ)+⋯.

Of or relating to Johann Peter Gustav Lejeune Dirichlet (1805–1859), German mathematician who made deep contributions to number theory.