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Mean Values of Cubic and Quartic Dirichlet Characters [PDF]

Functiones Et Approximatio, Commentarii Mathematici, 2020
12 ...
Lee Zhao
exaly   +6 more sources

A Note on the Dirichlet Characters of Polynomials

Mathematica Slovaca, 2014
Abstract The main purpose of this paper is using the analytic methods and the properties of character sums to study the computational problem of several kind character sums of polynomials mod q, an odd square-full number, and give two interesting identities for them.
Wenpeng Zhang
exaly   +2 more sources

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ON DIRICHLET CHARACTERS OF POLYNOMIAL

Bulletin of the London Mathematical Society, 2002
The classical result, due to Pólya and Vinogradov, is that the estimates \[ \sum_{n=N+1}^{N+H}\chi(n)\ll q^{1/2}\log q \] holds for all nonprincipal Dirichlet characters \(\chi\) modulo \(q\). The main result of the note under review is to show that for certain primitive characters \(\chi\) modulo \(q\) and some special polynomials \(f(x)\) with ...
Zhang, Wenpeng, Yi, Yuan
openaire   +1 more source

Dirichlet Expression for L(1, χ) With General Dirichlet Character

Proceedings of the Indian Academy of Sciences: 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.
exaly   +2 more sources

On Dirichlet Characters of Polynomials

Proceedings of the London Mathematical Society, 1963
Let \(q\) be a fixed positive integer and \(f(x)\) a nonlinear product of rational linear polynomials which is not a perfect \(q\)-th power. Let \(A\ll B\) mean \(A < k\vert B\vert\) for some positive constant \(k\). Theorem 1. For \(\varepsilon > 0\) if \(p\equiv 1\pmod q\) is a sufficiently large prime and \(\chi\) is a \(q\)-th order character ...
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On Primitivity of Dirichlet Characters

International Journal of Number Theory, 2015
Recall that a Dirichlet character is called imprimitive if it is induced from a character of smaller level, and otherwise it is called primitive. In this paper, we introduce a modification of "inducing to higher level" which causes imprimitive characters to behave primitively, in the sense that the properties of the associated Gauss sum and the ...
Daileda, R., Jones, N.
exaly   +2 more sources

Signatures of Dirichlet characters and elliptic curves

Journal of Number Theory, 2021
The authors study on signatures of the Dirichlet characters associated with elliptic curves. They find a lower bound for the number of conductors $q\leq Q$ with $q\equiv 1\pmod n$ having $k$ prime divisors of the Dirichlet characters $\chi$ of fixed order $n$ and with given values $\chi(m)$ for primes $m\leq b$. They introduce an elliptic curve variant
Pomykała, Jacek, Dąbrowski, Andrzej
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Sums with convolutions of Dirichlet characters

manuscripta mathematica, 2010
Let \(\chi_1\) and \(\chi_2\) be primitive Dirichlet characters with conductors \(q_1\) and \(q_2\), respectively, and let \[ S_{\chi_1,\chi_2}(X):=\sum_{ab\leq X}\chi_1(a)\chi_2(b). \] The authors prove that if \(X\geq q_2^{\frac 23}\geq q_1^{\frac 23}\) and \(\log X=q_2^{o(1)}\), then \[ \left| S_{\chi_1,\chi_2}(X)\right|\leq X^{\frac {13}{18}}q_1 ...
Banks, William D., Shparlinski, Igor E.
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