Search

Let r be a positive integer ≥2. We consider a family of primitive Dirichlet characters of order r with conductor co-prime to r. For this family, we compute the one-level density with explicit lower order terms in two ways, using Weil's explicit formula and the Ratios conjecture. Also, the n -level density for the family twisted by a fixed cuspidal automorphic representation π of G L M (A Q) is obtained. It turns out that, when r ≥ 3 , the symmetry type for our family is always unitary. [ABSTRACT FROM AUTHOR]

Let q ≥ 3 be an integer, χ denote a Dirichlet character modulo q , for any real number a ≥ 0 , we define the generalized Dirichlet L -functions L (s , χ , a) = ∑ n = 1 ∞ χ (n) (n + a) s , where s = σ + i t with σ > 1 and t both real. It can be extended to all s by analytic continuation. In this paper, we study the mean value properties of the generalized Dirichlet L -functions, and obtain several sharp asymptotic formulae by using analytic method. [ABSTRACT FROM AUTHOR]

In the paper, a limit theorem for weakly convergent probability measures on the complex plane for twisted with Dirichlet characterL-functions of elliptic curves with an increasing modulus of the character is proved. [ABSTRACT FROM PUBLISHER]

In this paper, we prove a multidimensional limit theorem for moduli of twists ofL-functions of elliptic curves. The limit measure in this theorem is defined by the characteristic transforms. [ABSTRACT FROM PUBLISHER]

In the paper, a limit theorem for the argument of twisted with Dirichlet character L-functions of elliptic curves with an increasing modulus of the character is proved. [ABSTRACT FROM PUBLISHER]

We obtain a limit theorem for L-functions of elliptic curves twisted by Dirichlet characters with increasing modulus. [ABSTRACT FROM AUTHOR]

Abstract: The main purpose of this paper is using the estimate for character sums and the analytic method to study the mean value of the Dirichlet L-functions with the weight of character sums, and give an interesting mean value theorem. [Copyright &y& Elsevier]

Let m 1 , ⋯ , m r be nonnegative integers, and set: M r = m 1 + ⋯ + m r. In this paper, first we establish an explicit linear decomposition of: ∏ i = 1 r B m i (x) m i ! in terms of Bernoulli polynomials B k (x) with 0 ≤ k ≤ M r . Second, for any integer q ≥ 2 , we study the mean values of the Dirichlet L-functions at negative integers: ∑ χ 1 , ⋯ , χ r (mod q) ; χ 1 ⋯ χ r = 1 ∏ i = 1 r L (− m i , χ i) where the summation is over Dirichlet characters χ i modulo q. Incidentally, a part of our work recovers Nielsen's theorem, Nörlund's formula, and its generalization by Hu, Kim, and Kim. [ABSTRACT FROM AUTHOR]