10.46298/hrj.2010.168
https://hrj.episciences.org/168
Montgomery, hugh L
hugh L
Montgomery
The combinatorics of moment calculations
In this paper, we consider the distribution of primes in intervals of length $\asymp\log x$; this leads to insights concerning Poisson random variables. Later, we consider reduced residues $({\rm mod}\,q)$ in short intervals, which similarly motivates us to derive further information concerning moments of binomial random variables. This discussion is extended further, where we consider the distribution of primes in intervals of length $\asymp x^{\theta}$ where $0<\theta<1$. Our analysis gives rise to a family of polynomials.
episciences.org
moments of binomial random variables
reduced residues
rimes in short intervals
[MATH] Mathematics [math]
2015-06-12
2010-01-01
2010-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01112382v1
2804-7370
https://hrj.episciences.org/168/pdf
VoR
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Hardy-Ramanujan Journal
Volume 33 - 2010
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