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pro vyhledávání: '"LAPORTA, MAURIZIO"'
We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof of a theorem of Gronwall on the asymptotic of the divisor functions.
Externí odkaz:
http://arxiv.org/abs/2306.17781
Autor:
Laporta, Maurizio
A celebrated theorem of Delange gives a sufficient condition for an arithmetic function to be the sum of the associated Ramanujan expansion with the coefficients provided by a previous result of Wintner. By applying the Delange theorem to the correla
Externí odkaz:
http://arxiv.org/abs/2204.01581
Autor:
Laporta, Maurizio
A celebrated conjecture of Hardy and Littlewood provides with an asymptotic formula for the counting function of the twin primes. We give an unconditional proof of such a formula by means of a finite Ramanujan expansion of the counting function expre
Externí odkaz:
http://arxiv.org/abs/2006.04547
Akademický článek
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Autor:
Coppola, Giovanni, Laporta, Maurizio
Publikováno v:
Indian J Pure Appl Math 49.2 (2018), 301-311
An arithmetic function $f$ is called a $sieve$ $function$ of $range$ $Q$ if its Eratosthenes transform $g=f\ast\mu$ has support in $[1,Q]$, where $g(q)\ll_{\varepsilon} q^{\varepsilon}$ ($\forall\varepsilon>0$). We continue our study of the distribut
Externí odkaz:
http://arxiv.org/abs/1612.08628
Autor:
Coppola, Giovanni, Laporta, Maurizio
Publikováno v:
Anal. Probab. Methods Number Theory, 25-28, (Palanga 2016 Conference Proceedings), A. Dubickas et al. (Eds), 2017 Vilnius University
We prove an upper bound for the exponential sum associated to a localized $k-$divisor function, i.e., the counting function of the number of ways to write a positive integer $n$ as a product of $k\ge 2$ positive integers, each of them belonging to a
Externí odkaz:
http://arxiv.org/abs/1512.01128
Autor:
Coppola, Giovanni, Laporta, Maurizio
For a real-valued and essentially bounded arithmetic function $f$, i.e., $f(n)\ll_{\varepsilon}\!n^{\varepsilon},\,\forall\varepsilon\!>\!0$, we \enspace give some optimal links between non-trivial bounds for the sums $\sum_{h\le H}\sum_{N
Externí odkaz:
http://arxiv.org/abs/1505.04551
Autor:
Coppola, Giovanni, Laporta, Maurizio
Publikováno v:
Hardy-Ramanujan Journal 39 (2016), 21-37
An arithmetic function $f$ is called a {\it sieve function of range} $Q$, if its Eratosthenes transform $g=f\ast\mu$ is supported in $[1,Q]\cap\N$, where $g(q)\ll_{\varepsilon} q^{\varepsilon}$ ($\forall\varepsilon>0$). Here, we study the distributio
Externí odkaz:
http://arxiv.org/abs/1503.07502
Autor:
Coppola, Giovanni, Laporta, Maurizio
Publikováno v:
Siauliai Math. Semin. 10 (18) (2015), 29-47
First we generalize a famous lemma of Gallagher on the mean square estimate for exponential sums by plugging a weight in the right hand side of Gallagher's original inequality. Then we apply it in the special case of the Cesaro weight, in order to es
Externí odkaz:
http://arxiv.org/abs/1411.1739
Autor:
Coppola, Giovanni, Laporta, Maurizio
Publikováno v:
Proc. Steklov Inst. Math. 299.1 (2017), 56-77
The weighted Selberg integral is a discrete mean-square, that is a generalization of the classical Selberg integral of primes to an arithmetic function $f$, whose values in a short interval are suitably attached to a weight function. We give conditio
Externí odkaz:
http://arxiv.org/abs/1312.5701