Zobrazeno 1 - 10
of 97
pro vyhledávání: '"Gambini, Alessandro"'
Publikováno v:
Indian Journal of Pure and Applied Mathematics, 1-12 (2023)
We explore a conjecture posed by Eswarathasan and Levine on the distribution of $p$-adic valuations of harmonic numbers $H(n)=1+1/2+\cdots+1/n$ that states that the set $J_p$ of the positive integers $n$ such that $p$ divides the numerator of $H(n)$
Externí odkaz:
http://arxiv.org/abs/2303.15010
In this paper we extend and improve all the previous results known in literature about weighted average, with Ces\`aro weight, of representations of an integer as sum of a positive arbitrary number of prime powers and a non-negative arbitrary number
Externí odkaz:
http://arxiv.org/abs/2012.02503
Publikováno v:
Canadian Mathematical Bulletin, 2021
We investigate the distribution of the digits of quotients of randomly chosen positive integers taken from the interval $[1,T]$, improving the previously known error term for the counting function as $T\to+\infty$. We also resolve some natural varian
Externí odkaz:
http://arxiv.org/abs/2008.09971
In this paper we provide some relationships between Catalan's constant and the $_3{\rm F}_2$ and $_4{\rm F}_3$ hypergeometric functions, deriving them from some parametric integrals. In particular, using the complete elliptic integral of the first ki
Externí odkaz:
http://arxiv.org/abs/2005.04672
Publikováno v:
Rendiconti Sem. Mat. Univ. Pol. Torino 78.1 (2020), 125-141
We give some theoretical and computational results on "random" harmonic sums with prime numbers, and more generally, for integers with a fixed number of prime factors.
Comment: Improvement form previous version with an addendum by J. Benatar and
Comment: Improvement form previous version with an addendum by J. Benatar and
Externí odkaz:
http://arxiv.org/abs/1911.11969
Publikováno v:
Int. Journal Number Theory 2021
We consider weighted averages of the number of representations of an even integer as a sum of two prime numbers, where each summand lies in a given arithmetic progression modulo a common integer $q$. Our result is uniform in a suitable range for $q$.
Externí odkaz:
http://arxiv.org/abs/1911.07220
Publikováno v:
Functiones et Approximatio Commentarii Mathematici 63.2 (2020), 215-226
We continue investigations on the average number of representations of a large positive integer as a sum of given powers of prime numbers. The average is taken over a short interval, whose admissible length depends on whether or not we assume the Rie
Externí odkaz:
http://arxiv.org/abs/1901.04481
Publikováno v:
Ramanujan J. 53.1 (2020), 155-166
We continue our recent work on averages for ternary additive problems with powers of prime numbers.
Comment: arXiv admin note: substantial text overlap with arXiv:1805.09008
Comment: arXiv admin note: substantial text overlap with arXiv:1805.09008
Externí odkaz:
http://arxiv.org/abs/1810.03020
Publikováno v:
Proc. Amer. Math. Soc. 148.4 (2020), 1499-1508
We investigate the average number of representations of a positive integer as the sum of $k + 1$ perfect $k$-th powers of primes. We extend recent results of Languasco and the last Author, which dealt with the case $k = 2$ [6] and $k = 3$ [5] respect
Externí odkaz:
http://arxiv.org/abs/1805.09008