Results 1 to 10 of about 19,492 (245)
Multiple Lucas–Dirichlet Series Associated With Additive and Dirichlet Characters [PDF]
Mediterranean Journal of Mathematics, 2021 20 ...
N. K. Meher, S. S. Rout
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Dirichlet Characters, Gauss Sums, and Inverse Z Transform [PDF]
Abstract and Applied Analysis, 2012 A generalized Möbius transform is presented. It is based on Dirichlet characters. A general algorithm is developed to compute the inverse Z transform on the unit circle, and an error estimate is given for the truncated series representation.
Jing Gao, Huaning Liu
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A generalization of Menon's identity with Dirichlet characters [PDF]
International Journal of Number Theory, 2018 The classical Menon's identity [7] states that \begin{equation*}\label{oldbegin1} \sum_{\substack{a\in\Bbb Z_n^\ast }}\gcd(a -1,n)=\varphi(n) \sigma_{0} (n), \end{equation*} where for a positive integer $n$, $\Bbb Z_n^\ast$ is the group of units of the
Hu, Xiaoyu, Kim, Daeyeoul, Li, Yan
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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 ...
Fischler, Stéphane
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The mean value of the function d(n)/d*(n) in arithmetic progressions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let d(n) and d*(n) be, respectively, the number of divisors and the number of unitary divisors of an integer n≥1. A divisor d of an integer is to be said unitary if it is prime over n/d.
Ouarda Bouakkaz, Abdallah Derbal
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Universality of Dirichlet L-functions with shifted characters
Lietuvos Matematikos Rinkinys, 2004 We study Dirichlet L-functions with shifted characters L(s, χ, H) = ⅀∞n=1 χ(n+H) ∕ ns, where H is an integer. Here we obtain a joint universality theorem for such functions.
Ramūnas Garunkštis
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Exceptional characters and nonvanishing of Dirichlet L-functions [PDF]
Mathematische Annalen, 2021 Let $ $ be a real primitive character modulo $D$. If the $L$-function $L(s, )$ has a real zero close to $s=1$, known as a Landau-Siegel zero, then we say the character $ $ is exceptional. Under the hypothesis that such exceptional characters exist, we prove that at least fifty percent of the central values $L(1/2, )$ of the Dirichlet $L$-functions $
Hung M. Bui +2 more
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An orthogonality relation for $\mathrm {GL}(4, \mathbb R) $ (with an appendix by Bingrong Huang)
Forum of Mathematics, Sigma, 2021 Orthogonality is a fundamental theme in representation theory and Fourier analysis. An orthogonality relation for characters of finite abelian groups (now recognized as an orthogonality relation on $\mathrm {GL}(1)$) was used by Dirichlet to prove ...
Dorian Goldfeld +2 more
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Average value of the divisor class numbers of real cubic function fields
Open Mathematics, 2023 We compute an asymptotic formula for the divisor class numbers of real cubic function fields Km=k(m3){K}_{m}=k\left(\sqrt[3]{m}), where Fq{{\mathbb{F}}}_{q} is a finite field with qq elements, q≡1(mod3)q\equiv 1\hspace{0.3em}\left(\mathrm{mod}\hspace{0 ...
Lee Yoonjin, Lee Jungyun, Yoo Jinjoo
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A Bound for a Sum of Products of Two Characters and Its Application
Mathematics, 2023 Using the exponent pair method, a bound is derived for the sum ∑manb≤xχ1a(m)χ2b(n), where a,b are fixed positive integers, χ1,χ2 are primitive Dirichlet characters modulo q1 and q2, respectively, and χ1a,χ2b are not principal characters.
Teerapat Srichan
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