In mathematics, the L-functions of number theory are expected to have several characteristic properties, one of which is that they satisfy certain ... Introduction · Theory of functional equations

The formula shows that the L-function of χ is equal to the L-function of the primitive character which induces χ, multiplied by only a finite number of factors. Functional equation · Relation to the Hurwitz zeta...

The functional equations relates Λ(χ, s) to Λ(χ, 1 − s) and involves a ”root number” τ(χ)/√q. . This is the Generalized Riemann Hypothesis.

$L$-functions satisfy the functional equation $\displaystyle \pi^{-\frac{s}{2}}\Gamma(\frac{s}{2}+a)L(s,\chi) \cr$ where $a=0$

All known analytic L-functions have a functional equation that can be written in the form Λ ( s ) : = N s / 2 ∏ j = 1 J Γ R ( s + μ j ) ∏ k = 1 K Γ C ( s + ...

30 окт. 2012 г. · Λ(X, s) = (X)Λ(X∗,k − s). In the case where L(X, s) admits (or is expected to admit) such a functional equation, the vertical line {s ∈ C | ...

The functional equation of the L-function associated to ω is. L(s, ω) = ε(s, ω) L(1 − s, eω). This theorem is a rather easy consequence of the first theorem ...

11 мар. 2022 г. · Functional equation for L-function · 1. If χ is not primitive then χ(n)=ψ(n)1gcd(n,r)=1 with ψ primitive so that L(s,χ)=L(s,ψ)∏p|r(1−ψ(p)p−s) · 2. Need reference for proof of functional equation for generalized ... Approximate functional equation of Selberg Class L-functions Approximate functional equation of the L function Functional equation of the Hecke L function in ideal term and ... Другие результаты с сайта math.stackexchange.com

The functional equation for Dirichlet's L functions was first given by Hurwitz in 1882 (Werke I, pp. 72–88), though he confined himself to real characters ...

26 мар. 2023 г. · L(s,χ)=s∞∫1∑n≤uχ(n)u−s−1du. Since the sum in the integrand is bounded, this formula gives an analytic continuation of L(s,χ) to a regular ...