Zobrazeno 1 - 10
of 63
pro vyhledávání: '"11N37, 11M06"'
Publikováno v:
Acta Arithmetica, 216.4(2024), 291-327
Let $\Delta_{k}(x)$ be the error term in the classical asymptotic formula for the sum $\sum_{n\leq x}d_{k}(n)$, where $d_{k}(n)$ is the number of ways $n$ can be written as a product of $k$ factors. We study the analytic properties of the Dirichlet s
Externí odkaz:
http://arxiv.org/abs/2412.11069
Autor:
Baluyot, Siegfred, Castillo, Cruz
We study the function $\Delta_k(x):=\sum_{n\leq x} d_k(n) - \mbox{Res}_{s=1} ( \zeta^k(s) x^s/s )$, where $k\geq 3$ is an integer, $d_k(n)$ is the $k$-fold divisor function, and $\zeta(s)$ is the Riemann zeta-function. For a large parameter $X$, we s
Externí odkaz:
http://arxiv.org/abs/2302.08003
Autor:
Billal, Masum
In a paper in the American Mathematical Monthly, the corresponding author asks for an asymptotic of a gcd-sum function \begin{align}\sum_{ab\leq N}\tau(\gcd(a,b))\label{eqn:taugcdsum}\end{align} We extensively study generalizations of the sum in the
Externí odkaz:
http://arxiv.org/abs/2206.05023
Autor:
Smith, Kevin, Andrade, Julio
We establish asymptotic formulae for various correlations involving general divisor functions $d_k(n)$ and partial divisor functions $d_l(n,A)=\sum_{q|n:q\leq n^A}d_{l-1}(q)$, where $A\in[0,1]$ is a parameter and $k,l\in\mathbb{N}$ are fixed. Our res
Externí odkaz:
http://arxiv.org/abs/1903.01566
We consider fluctuations of error terms $\Delta(x)$ appearing in the asymptotic formula for a summatory function of coefficients of the Dirichlet series. These are quantified via $\Omega$ and $\Omega_{\pm}$ estimates. We obtain $\Omega$ bounds for Le
Externí odkaz:
http://arxiv.org/abs/1512.03144
Autor:
Ivić, Aleksandar
Publikováno v:
Novi Sad J. of Math. 45(2015), Vol. 1, 31-44
In this overview paper, presented at the meeting DANS14, Novi Sad, July3-7, 2014, we give some applications of Laplace transforms to analytic number theory. These include the classical circle and divisor problem, moments of $|\zeta(1/2+it)|$, and a d
Externí odkaz:
http://arxiv.org/abs/1409.0331
Autor:
Lelechenko, Andrew V.
Publikováno v:
Siauliai Math. Semin., 2015, vol. 10 (18), p. 181-197
Consider the operator $E$ on arithmetic functions such that $Ef$ is the multiplicative arithmetic function defined by $(Ef)(p^a) = f(a)$ for every prime power $p^a$. We investigate the behaviour of $E^m\tau_k$, where $\tau_k$ is a $k$-dimensional div
Externí odkaz:
http://arxiv.org/abs/1307.3683
Autor:
Coppola, Giovanni
We give a new non-trivial upper bound for the Selberg integral of the three-divisor function $d_3(n)$. Our method applies our recent conjecture together with Laporta, for the modified Selberg integral of $d_3(n)$, and a kind of modified Gallagher Lem
Externí odkaz:
http://arxiv.org/abs/1207.0902
Autor:
Coppola, Giovanni, Laporta, Maurizio
Publikováno v:
Journal of Numbers Volume 2014(2014),Article ID 140840,13 pages
The present paper is a dissertation on the possible consequences of a conjectural bound for the so-called \thinspace modified Selberg integral of the divisor function $d_3$, i.e. a discrete version of the classical Selberg integral, where $d_3(n)=\su
Externí odkaz:
http://arxiv.org/abs/1205.1706
We investigate the first and second moments of shifted convolutions of the generalised divisor function $d_3(n)$.
Comment: 22 pages
Comment: 22 pages
Externí odkaz:
http://arxiv.org/abs/1101.5464