Zobrazeno 1 - 10
of 346
pro vyhledávání: '"30b50"'
Autor:
Broucke, Frederik, Hilberdink, Titus
In this paper we obtain a mean value theorem for a general Dirichlet series $f(s)= \sum_{j=1}^\infty a_j n_j^{-s}$ with positive coefficients for which the counting function $A(x) = \sum_{n_{j}\le x}a_{j}$ satisfies $A(x)=\rho x + O(x^\beta)$ for som
Externí odkaz:
http://arxiv.org/abs/2409.06301
Autor:
Marchionna, Bianca
We study the double-coset zeta functions for groups acting on trees, focusing mainly on weakly locally $\infty$-transitive or (P)-closed actions. After giving a geometric characterisation of convergence for the defining series, we provide explicit de
Externí odkaz:
http://arxiv.org/abs/2409.01860
Autor:
Favorov, Serhii
We study a certain family of discrete measures with unit masses on a horizontal strip as an analogue of Fourier quasicrystals on the real line. We prove a one-to-one correspondence between supports of measures from this family and zero sets of expone
Externí odkaz:
http://arxiv.org/abs/2408.09563
Autor:
Berg, Christian
We consider a normalized indeterminate Hamburger moment sequence s which is supposed to be Stieltjes. We revisit old results about determinacy/indeterminacy in the sense of Stieltjes for s and we prove some new results about the concepts involved.
Externí odkaz:
http://arxiv.org/abs/2407.08511
Given a frequency $\lambda=(\lambda_n)$, we consider the Hardy spaces $ \mathcal{H}_p^\lambda$ of $\lambda$-Dirichlet series $ D = \sum_n a_n e^{-\lambda_n s}$ and study the asymptotic behavior of the upper and lower democracy functions of its canoni
Externí odkaz:
http://arxiv.org/abs/2406.03623
Autor:
Elaissaoui, Lahoucine
In order to well understand the behaviour of the Riemann zeta function inside the critical strip, we show; among other things, the Fourier expansion of the $\zeta^k(s)$ ($k \in \mathbb{N}$) in the half-plane $\Re s > 1/2$ and we deduce a necessary an
Externí odkaz:
http://arxiv.org/abs/2406.00331
Autor:
Favorov, Serhii
We study properties of temperate non-negative purely atomic measures in the Euclidean space such that the distributional Fourier transform of these measures are pure point ones. A connection between these measures and almost periodicity is shown, sev
Externí odkaz:
http://arxiv.org/abs/2404.15448
Autor:
Angot, Philippe
We give a simple Tauberian proof of the Prime Number Theorem using only elementary real analysis. Hence, the analytic continuation of Riemann's zeta function $\zeta$ and its non-vanishing value on the whole line $\{z\in {\mathbb C};\,{\mathrm{Re}\,}
Externí odkaz:
http://arxiv.org/abs/2404.13019
Autor:
Brudnyi, Alexander, Sasane, Amol
Let $\mathscr O_u$ be the algebra of holomorphic functions on ${\bf C}_+:=\{s\in{\bf C}:\text{Re }s>0\}$ that are limits of Dirichlet series $D=\sum_{n=1}^\infty a_n n^{-s}$, $s\in \bf{C}_+$, that converge uniformly on proper half-planes of $\bf{C}_+
Externí odkaz:
http://arxiv.org/abs/2404.03616