Results 11 to 20 of about 37,887 (268)

Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Open Mathematics
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
doaj   +2 more sources

Two identities related to dirichlet character of polynomials [PDF]

Czechoslovak Mathematical Journal, 2013
The authors study sums, analogous to Kloosterman sums. They prove two theorems: Theorem 1. Let \(q\) be an odd number, \(\chi \) be a Dirichlet character mod \(q\), \(k\) and \(m\) be positive integers such that \((km,q)=1\) and \((k+1,\varphi (q))=1\). Then for any primitive character \(\chi \bmod q\), we have the identity \[ | C(\chi ,k,m;q)| = \left|
Yao, Weili, Zhang, Wenpeng
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Dirichlet expression for L(1, χ) with general Dirichlet character

Proceedings - Mathematical Sciences, 2010
In the famous work of Dirichlet on class number formula, L(s, χ) at s = 1 has been expressed as a finite sum, where L(s, χ) is the Dirichlet L-series of a real Dirichlet character. We show that this expression with obvious modification is valid for the general primitive Dirichlet character χ.
openaire   +3 more sources

Dirichlet L-functions and character power sums

Journal of Number Theory, 1970
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Modified Dirichlet Character Sums over the k-free Integers

Bulletin of the Brazilian Mathematical Society, New Series
19 pages.
openaire   +4 more sources

Large character sums: Burgess's theorem and zeros of $L$-functions [PDF]

, 2017
We study the conjecture that $\sum_{n\leq x} \chi(n)=o(x)$ for any primitive Dirichlet character $\chi \pmod q$ with $x\geq q^\epsilon$, which is known to be true if the Riemann Hypothesis holds for $L(s,\chi)$.
Granville, Andrew, Soundararajan, Kannan
core   +2 more sources

Value-distribution of twisted L-functions of normalized cusp forms

Lietuvos Matematikos Rinkinys, 2010
A limit theorem in the sense of weak convergence of probability measures on the complex plane for twisted with Dirichlet character L-functions of holomorphic normalized Hecke eigen cusp forms with an increasing modulus of the character is proved.
Alesia Kolupayeva
doaj   +1 more source

A transformation formula with primitive character

Lietuvos Matematikos Rinkinys, 2013
We prove a transformation formula for the exponential sum involving the divisor function, and primitive character modulo q. This formula can be applied to obtain meromorphic continuation for the Mellin transform of the square of Dirichlet L-function with
Aidas Balčiūnas
doaj   +1 more source

Mellin Transform of Dirichlet L-Functions with Primitive Character

Mathematical Modelling and Analysis, 2014
In the paper, meromorphic continuation for the modified Mellin transform of Dirichlet L-functions with primitive character is obtained.
Aidas Balčiūnas, Darius Šiaučiūnas
doaj   +1 more source

Maass Spezialschar of level N [PDF]

, 2016
In this paper the image of the Saito-Kurokawa lift of level $N$ with Dirichlet character is studied. We give a new characterization of this so called Maass Spezialschar of level $N$ by symmetries involving Hecke operators related to $\Gamma_0(N)$.
Heim, B.
core   +3 more sources