English Dictionary

Dirichlet series

名詞

可算名詞 不可算名詞

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

日本語の意味

ディリクレ級数：数論で扱われる無限級数であり、各項が aₙ/nˢ の形を取り、ここで s および各 aₙ は複素数となる。

Dirichlet series often appear in analytic number theory when studying L-functions and multiplicative arithmetic functions.

ディリクレ級数は、L関数や乗法的算術関数を研究する際に解析的整数論でよく現れます。

意味（1）

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

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.

Dirichlet series （ plural ）