Word Pronunciation & Dictionary

dirichlet series

Word Rarity Very rare

Frequency: Zipf frequency 2.22 in modern English

Syllables: dirich-let series
IPA

21

Scrabble Score

15

Letters

2

Syllables

9

Unique Chars

Meaning

noun

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

Countable; Uncountable

Example Sentences

"Traditionally, starting from Euler, multiplicativity of arithmetic sequences is customarily expressed in the form of an Euler product factorization of the generating Dirichlet series. It turns out that in the situation of modular forms, suitable Dirichlet series constructed by Fourier coefficients of eigenfunctions of Hecke operators can be expressed through Dirichlet series formed by the corresponding eigenvalues."
"We have now given heuristically a large family of multiple Dirichlet series, one for each simply laced Dynkin diagram."
"2014, Marius Overholt, A Course in Analytic Number Theory, American Mathematical Society, page 157, The sum A(s)=∑ₙ₌₁ ᪲a_nn⁻ˢ of a convergent Dirichlet series is a holomorphic (single-valued analytic) function in the half plane σ>σ_c(A), and the terms of the Dirichlet series are holomorphic in the whole complex plane, and the series converges uniformly on every compact subset of σ>σ_c(A) by Proposition 3.3."

Etymology

Named after German mathematician Peter Gustav Lejeune Dirichlet (1805–1859).

Usage

Inflected Forms

Dirichlet's series (alternative)

Phrases

Dirichlet L-series Dirichlet function Dirichlet L-function Riemann zeta function

Frequently Paired Words

Dirichlet L-series Dirichlet function Dirichlet L-function Riemann zeta function

Synonyms

general Dirichlet series ordinary Dirichlet series

Questions

What does dirichlet series mean?: Any infinite series of the form ∑ₙ₌₁ ᪲(a_n)/(nˢ), where s and each a_n are complex numbers.
Where does dirichlet series come from?: Named after German mathematician Peter Gustav Lejeune Dirichlet (1805–1859).

How to pronounce dirichlet series

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