Results 211 to 220 of about 19,492 (245)
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On pseudorandom properties of some Dirichlet characters
The Ramanujan Journal, 2007The author of this paper studies binary sequences \[ E_N=(e_1,\ldots,e_N)\in\{-1,+1\}^N \] and deals with two quantities for measuring their pseudorandomness, namely the so-called well-distribution measure and the correlation measure. These quantities were introduced by Mauduit and Sárközy. In this article, two main results are shown. First, the author
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Analytic properties of multiple Dirichlet series associated to additive and Dirichlet characters
manuscripta mathematica, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Biswajyoti Saha
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ON DIRICHLET CHARACTERS OF POLYNOMIAL
Bulletin of the London Mathematical Society, 2002The 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
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On primitivity of Dirichlet characters
International Journal of Number Theory, 2015Recall 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.
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Acta Arithmetica, 1999
Let \(\chi\) be a Dirichlet character of conductor \(p^n\) with \(p \in {\mathbb{P}}\), \(n \in {\mathbb{N}}\), and let \(f(x) = a_0 + a_1 x + \cdots + a_k x^k\) be an integral polynomial such that \(k>3\) and \((p^n,a_1,\ldots,a_k)= p^m\). Using a special iteration the author proves some general character sum estimates of type \[ p^{-(n-m)(1-1/k ...
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Let \(\chi\) be a Dirichlet character of conductor \(p^n\) with \(p \in {\mathbb{P}}\), \(n \in {\mathbb{N}}\), and let \(f(x) = a_0 + a_1 x + \cdots + a_k x^k\) be an integral polynomial such that \(k>3\) and \((p^n,a_1,\ldots,a_k)= p^m\). Using a special iteration the author proves some general character sum estimates of type \[ p^{-(n-m)(1-1/k ...
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On Dirichlet Characters of Polynomials
Proceedings of the London Mathematical Society, 1963Let \(q\) 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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Sums with convolutions of Dirichlet characters
manuscripta mathematica, 2010Let \(\chi_1\) 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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Mean value of real Dirichlet characters using a double Dirichlet series
Canadian Mathematical Bulletin, 2023AbstractWe study the double character sum $\sum \limits _{\substack {m\leq X,\\m\mathrm {\ odd}}}\sum \limits _{\substack {n\leq Y,\\n\mathrm {\ odd}}}\left (\frac {m}{n}\right )$ and its smoothly weighted counterpart. An asymptotic formula with power saving error term was obtained by Conrey, Farmer, and Soundararajan by applying the Poisson ...
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-Adic Dirichlet characters of algebraic function fields
Journal of Soviet Mathematics, 1979A theory of precyclic P-extensions is developed which contains the well-known Witt theory. This theory makes it possible to describe so-called P-adic Dirichlet characters of function fields. In particular, for a trigonometric sum of the form where P is a prime number and f is a polynomial, its expression in terms of the zeros of a certain L function
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