Zobrazeno 1 - 10
of 20
pro vyhledávání: '"11N37, 11Y60"'
Autor:
Kiuchi, Isao, Eddin, Sumaia Saad
Let $\gcd(d_{1},\ldots,d_{k})$ be the greatest common divisor of the positive integers $d_{1},\ldots,d_{k}$, for any integer $k\geq 2$, and let $\tau$ and $\mu$ denote the divisor function and the M\"{o}bius function, respectively. For an arbitrary a
Externí odkaz:
http://arxiv.org/abs/2102.03714
Autor:
Kiuchi, Isao, Eddin, Sumaia Saad
Let $\mathbb{Z}_{m}$ be the additive group of residue classes modulo $m$. For any positive integers $m$ and $n$, let $s(m,n)$ and $c(m,n)$ denote the total number of subgroups and cyclic subgroups of the group ${\mathbb{Z}}_{m}\times {\mathbb{Z}}_{n}
Externí odkaz:
http://arxiv.org/abs/2008.07850
In this paper, we give various identities for the weighted average of the product of generalized Anderson-Apostol sums with weights concerning completely multiplicative function, completely additive function, logarithms, the Gamma function, Bernoulli
Externí odkaz:
http://arxiv.org/abs/1811.06022
Publikováno v:
J. Number Theory 209 (2020), 147-166
The Jordan totient $J_k(n)$ can be defined by $J_k(n)=n^k\prod_{p\mid n}(1-p^{-k})$. In this paper, we study the average behavior of fractions $P/Q$ of two products $P$ and $Q$ of Jordan totients, which we call Jordan totient quotients. To this end,
Externí odkaz:
http://arxiv.org/abs/1810.04742
Autor:
Kiuchi, Isao, Eddin, Sumaia Saad
Let $\gcd(k,j)$ be the greatest common divisor of the integers $k$ and $j$. For any arithmetical function $f$, we establish several asymptotic formulas for weighted averages of gcd-sum functions with weight concerning logarithms, that is $$\sum_{k\le
Externí odkaz:
http://arxiv.org/abs/1804.01902
Autor:
Kiuchi, Isao, Eddin, Sumaia Saad
Let $\gcd(j,k)$ be the greatest common divisor of the integers $j$ and $k$. In this paper, we give several interesting asymptotic formulas for weighted averages of the $\gcd$-sum function $f(\gcd(j,k)) $ and the function $\sum_{d|k, d^{s}|j}(f*\mu)(d
Externí odkaz:
http://arxiv.org/abs/1801.03647
Autor:
Moree, Pieter
Publikováno v:
Irregularities in the Distribution of Prime Numbers - Research Inspired by Maier's Matrix Method, Eds. J.~Pintz and M.~Th.~Rassias, Springer, 2018, 143--163
Kummer (1851) and, many years later, Ihara (2005) both posed conjectures on invariants related to the cyclotomic field $\mathbb Q(\zeta_q)$ with $q$ a prime. Kummer's conjecture concerns the asymptotic behaviour of the first factor of the class numbe
Externí odkaz:
http://arxiv.org/abs/1711.07996
Autor:
Moree, Pieter, Eddin, Sumaia Saad
Publikováno v:
Int. J. Number Theory 13 (2017), 2583--2596
In RSA cryptography numbers of the form $pq$, with $p$ and $q$ two distinct proportional primes play an important role. For a fixed real number $r>1$ we formalize this by saying that an integer $pq$ is an RSA-integer if $p$ and $q$ are primes satisfy
Externí odkaz:
http://arxiv.org/abs/1606.07727
Autor:
Moree, Pieter
Publikováno v:
Mathematics Newsletter 21, no. 3 (2011), 73-81
A set S of integers is said to be multiplicative if for every pair m and n of coprime integers we have that mn is in S iff both m and n are in S. Both Landau and Ramanujan gave approximations to S(x), the number of n<=x that are in S, for specific ch
Externí odkaz:
http://arxiv.org/abs/1110.0708
Publikováno v:
Math. Comp. 83 (2014), no. 287, 1447-1476
For a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n\le x such that q does not divide phi(n). Part of the analysis involves a careful study of the Euler-Kronecker constants for
Externí odkaz:
http://arxiv.org/abs/1108.3805