# principal character

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n]([chi]) denote the n-th Laurent-Stieltjes coefficients around s = 1 of the associated Dirichlet L-series for a given primitive Dirichlet character [chi] modulo q.
Let x be a primitive Dirichlet character to modulus q.
Where [chi] denotes a Dirichlet character modulo d, L(n, [chi]) denotes the Dirichlet L-function corresponding to[chi], [empty set](d) and [zeta](s) are the Euler function and Riemann zeta-function, respectively.
where x denotes a Dirichlet character modulo q, q [greater than or equal to] 2 is an integer, which is called as a sum analogues to character sums.
Zhang, Dirichlet characters and their applications, Science Press, Beijing, 2008.
Let [chi] be the Dirichlet character with conductor f [member of] N = {1, 2,.
where [chi] is a Dirichlet character with [chi] [not equal to] 1 with 1 denoting the principal character, its convergence in 0 < Re(s) < 1 is an unsolved problem.
The Riemann zeta or Dirichlet L-functions (X = Z, Prim(Z) = {prime numbers}, N(p) = p, [rho] = Dirichlet character, n = 1) and the Selberg zeta function (X = [GAMMA]: a Fuchsian group, Prim([GAMMA]) = {prime geodesics in [GAMMA]\H} with H the upper half plane, N(p) = [e.
where [chi] be the Dirichlet character mod p, L(1, [chi]) be the Dirichlet L-function corresponding character [chi] and a/p = [p.
Let p be an odd prime and [chi] be the Dirichlet character mod p.
For any positive integer number q > 3, let [chi] denote a Dirichlet character modulo q.

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