Get Math Help

GET TUTORING NEAR ME!

(800) 434-2582

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Home / Get Math Help

    Dirichlet L-series

    Definition

    A Dirichlet L-series is a series of the form L_k(s, χ) congruent sum_(n = 1)^∞ χ_k(n) n^(-s), where the number theoretic character χ_k(n) is an integer function with period k, are called Dirichlet L-series. These series are very important in additive number theory (they were used, for instance, to prove Dirichlet's theorem), and have a close connection with modular forms. Dirichlet L-series can be written as sums of Lerch transcendents with z a power of e^(2π i/k). Dirichlet L-series is implemented in the Wolfram Language as DirichletL[k, j, s] for the Dirichlet character χ(n) with modulus k and index j.

    Related Wolfram Language symbol

    DirichletL

    Associated person

    Lejeune Dirichlet

    Back to List | POWERED BY THE WOLFRAM LANGUAGE