Umberto Cerruti

activity

20112024

most citedPeriodic representations for cubic irrationalities

9 citations · 50 across the 23 of their papers we have counts for

collaborators

24 papers

math.NT2024

Algebraic integers with continued fraction expansions containing palindromes and square roots with prescribed periods

Stefano Barbero, Umberto Cerruti, Nadir Murru +1

We present a characterization of the algebraic integers with continued fraction expansions of the form $[a_{0}, a_{1}, \dots, a_{n}, s]$ , where $(a_{1}, \dots, a_{n})$ is a pali…

cs.CR2021

One Time Pad and the Short Key Dream

Umberto Cerruti

This is a survey on the One Time Pad (OTP) and its derivatives, from its origins to modern times. OTP, if used correctly, is (the only) cryptographic code that no computing power,…

math.NT2020

An isomorphism between the convolution product and the componentwise sum connected to the D'Arcais numbers and the Ramanujan tau function

Stefano Barbero, Umberto Cerruti, Nadir Murru

Given a commutative ring $R$ with identity, let $H_{R}$ be the set of sequences of elements in $R$ . We investigate a novel isomorphism between $(H_{R}, +)$ and $(H ~_{R}, *)$ , where…

math.NT2020

Approximations of algebraic irrationalities with matrices

Stefano Barbero, Umberto Cerruti, Nadir Murru

We discuss the use of matrices for providing sequences of rationals that approximate algebraic irrationalities. In particular, we study the regular representation of algebraic exte…

math.NT2020

Linear fractional transformations and non-linear leaping convergents of some continued fractions

Christopher Havens, Stefano Barbero, Umberto Cerruti +1

For $α_{0} = [a_{0}, a_{1}, \dots]$ an infinite continued fraction and $σ$ a linear fractional transformation, we study the continued fraction expansion of $σ (α_{0})$ and its c…

math.NT2018★ 4 cited

On the operations of sequences in rings and binomial type sequences

Stefano Barbero, Umberto Cerruti, Nadir Murru

Given a commutative ring with identity $R$ , many different and interesting operations can be defined over the set $H_{R}$ of sequences of elements in $R$ . These operations can also g…