Phrase guide

Dirichlet series

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Usage: countable, uncountable

Topics: mathematics, number-theory, sciences

Examples

  • 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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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

Across languages

Translations

2 source translations are retained for this English entry.

  • Italian: serie di Dirichlet — infinite series
  • Polish: szereg Dirichleta — infinite series