In mathematics, a Dirichlet L-series is a function of the form L ( s , χ ) = ∑ n = 1 ∞ χ ( n ) n s . {\displaystyle L(s,\chi )=\sum _{n=1}^{\infty }{\frac...

is a Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function via analytic continuation. The Riemann zeta function is an...

It is a particular Dirichlet L-function, the L-function for the alternating character of period four. The Dirichlet beta function is defined as β ( s...

usually seen definition of the Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions. It is conjectured that the Selberg class of...

in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number...

all over the prime numbers. Arithmetic function Dirichlet L-function Dirichlet series Multiplicative function Apostol, Tom (1976). Introduction to Analytic...

missing. Explicit formula (L-function) Riemann–Siegel formula (particular approximate functional equation) "§25.15 Dirichlet -functions on NIST". Weisstein,...

a Dirichlet series, it has an Euler product expansion, it satisfies a functional equation, it has an analytic continuation to a meromorphic function on...

Dirichlet beta function Dirichlet L-function Hurwitz zeta function Legendre chi function Lerch transcendent Polylogarithm and related functions: Incomplete...

Riemann zeta function, such as Dirichlet series, Dirichlet L-functions and L-functions, are known. The Riemann zeta function ζ(s) is a function of a complex...

In mathematics, the Dirichlet convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory...

universality of zeta functions is the remarkable ability of the Riemann zeta function and other similar functions (such as the Dirichlet L-functions) to approximate...

Sequences. 13: Article 10.7.4. Apostol, T. M. (1997), "Modular Functions and Dirichlet Series in Number Theory", New York: Springer-Verlag 2nd Ed. Ashworth...

(a)te^{at}}{e^{ft}-1}}} for χ a Dirichlet character with conductor f. The Kubota–Leopoldt p-adic L-function Lp(s, χ) interpolates the Dirichlet L-function with the Euler...

was proved by Dirichlet (1837) with Dirichlet L-series. The proof is modeled on Euler's earlier work relating the Riemann zeta function to the distribution...

are called Dedekind zeta-functions), Maass forms, and Dirichlet characters (in which case they are called Dirichlet L-functions). When the Riemann hypothesis...

on the left-hand side is also L ( 1 ) {\displaystyle L(1)} where L ( s ) {\displaystyle L(s)} is the Dirichlet L-function for the field of Gaussian rational...

Johann Peter Gustav Lejeune Dirichlet (/ˌdɪərɪˈkleɪ/; German: [ləˈʒœn diʁiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician. In number...

mathematics, an Artin L-function is a type of Dirichlet series associated to a linear representation ρ of a Galois group G. These functions were introduced...

the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of the sinc function over...

generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of L-functions larger than Dirichlet L-functions, and a natural setting...

a complex-valued arithmetic function χ : Z → C {\displaystyle \chi :\mathbb {Z} \rightarrow \mathbb {C} } is a Dirichlet character of modulus m {\displaystyle...

"Table of Dirichlet L-series and prime zeta modulo functions for small moduli". arXiv:1008.2547 [math.NT]. Weisstein, Eric W. "Prime Zeta Function". MathWorld...

L series may refer to: L-series trains in China Saturn L series – sedans and station wagons L-function Honda L engine Nissan L engine Dirichlet L-function...

the Hurwitz zeta function may be expressed as a linear combination of Dirichlet L-functions and vice versa: The Hurwitz zeta function coincides with Riemann's...

Fourier series) Dirichlet L-function Dirichlet principle Dirichlet problem (partial differential equations) Dirichlet process Dependent Dirichlet process Hierarchical...

function f {\displaystyle f} and its Fourier transform, we get the formula above. The Riemann zeta function can be replaced by a Dirichlet L-function...

counterexample to the generalized Riemann hypothesis, on the zeros of Dirichlet L-functions associated to quadratic number fields. Roughly speaking, these are...

names: the popcorn function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function (not to be confused...

generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series. Every...