Results 31 to 40 of about 1,790 (152)
Generalized q-Euler Numbers and Polynomials of Higher Order and Some Theoretic Identities
Journal of Inequalities and Applications, 2010 We give a new construction of the q-Euler numbers and polynomials of higher order attached to Dirichlet's character χ. We derive some theoretic identities involving the generalized q-Euler numbers and polynomials of higher order.
T. Kim, Y. H. Kim
doaj +1 more source
Character sums over generalized Lehmer numbers
Journal of Inequalities and Applications, 2016 Let q > 2 $q>2$ be an integer, n ⩾ 2 $n\geqslant2$ be a fixed integer with ( n , q ) = 1 $(n,q)=1$ , ψ be a non-principal Dirichlet character modq. An upper bound estimate for character sums of the form ∑ a ∈ C ( 1 , q ) ψ ( a ) $$\sum_{a\in\textit{C}(1 ...
Yuankui Ma +3 more
doaj +1 more source
A note on the Dirichlet characters of polynomials [PDF]
Acta Arithmetica, 2004 This paper is a continuation of a paper of the first author together with \textit{Y. Yi} [Bull. Lond. Math. Soc. 34, 469--473 (2002; Zbl 1038.11052)]. The main result is a generalized identity of the form \[ \sum_{n=1}^{q}\chi\bigl(f(n)\bigr)= \varepsilon(\chi,f)\cdot q^{1/2} \] where \(q\) is a perfect square, \(\chi\) a primitive Dirichlet character ...
Zhang, Wenpeng, Yao, Weili
openaire +1 more source
On the first power mean of L-functions with the weight of general Kloosterman sums
International Journal of Mathematics and Mathematical Sciences, 2002 The main purpose of this paper is using the estimates for character sums and the analytic method to study the first power mean of Dirichlet L-functions with the weight of general Kloosterman sums, and give an interesting asymptotic formula.
Zhang Wenpeng
doaj +1 more source
Improving Online Clustering of Chinese Technology Web News With Bag-of-Near-Synonyms
IEEE Access, 2020 In the Internet era, online clustering of technology web news can help discover scientific breakthroughs and grasp technology trends. To do that automatically, the news documents to be clustered must be represented appropriately with numerical vectors ...
Zhe Zhang +4 more
doaj +1 more source
Mean Values of Products of L-Functions and Bernoulli Polynomials
Mathematics, 2018 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 !
Abdelmejid Bayad, Daeyeoul Kim
doaj +1 more source
High-Dimensional D. H. Lehmer Problem over Quarter Intervals
Abstract and Applied Analysis, 2014 The high-dimensional D. H. Lehmer problem over quarter intervals is studied. By using the properties of character sum and the estimates of Dirichlet L-function, the previous result is improved to be the best possible in the case of q = p, an odd prime ...
Tianping Zhang
doaj +1 more source
ON BINARY CORRELATIONS OF MULTIPLICATIVE FUNCTIONS
Forum of Mathematics, Sigma, 2018 We study logarithmically averaged binary correlations of bounded multiplicative functions $g_{1}$ and $g_{2}$ . A breakthrough on these correlations was made by Tao, who showed that the
JONI TERÄVÄINEN
doaj +1 more source
Irrationality of values of L‐functions of Dirichlet characters [PDF]
Journal of the London Mathematical Society, 2019 In a recent paper with Sprang and Zudilin, the following result was proved: if $a$ is large enough in terms of $\varepsilon>0$, then at least $2^{(1-\varepsilon)\frac{\log a}{\log \log a}}$ values of the Riemann zeta function at odd integers between $3$ and $a$ are irrational.
openaire +2 more sources
On Some Arithmetical Properties of the Genocchi Numbers and Polynomials
Advances in Difference Equations, 2008 We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function. We have the generating function of (h,q)-Genocchi polynomials.
Kyoung Ho Park, Young-Hee Kim
doaj +1 more source