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pro vyhledávání: '"D'Elia, Michele"'
Autor:
Elia, Michele
Legendre discovered that the continued fraction expansion of $\sqrt N$ having odd period leads directly to an explicit representation of $N$ as the sum of two squares. In this vein, it was recently observed that the continued fraction expansion of $\
Externí odkaz:
http://arxiv.org/abs/2103.14861
Autor:
Elia, Michele
Let $p$ be a prime, $m$ be a positive integer ( $m \geq 1$, and $m \geq 2$ if $p=2$), and $\chi_n$ be a multiplicative complex character on $\mathbb F^*_{p^m}$ with order $n| (p^m-1)$. We show that a partition $\mathcal A_1 \cup \mathcal A_2 \cup \cd
Externí odkaz:
http://arxiv.org/abs/2102.07411
In this paper, we highlight that the point group structure of elliptic curves over finite or infinite fields, may be also observed on singular cubics with a quadratic component. Starting from this, we are able to introduce in a very general way a gro
Externí odkaz:
http://arxiv.org/abs/2001.04288
Autor:
Elia, Michele
Legendre found that the continued fraction expansion of $\sqrt N$ having odd period leads directly to an explicit representation of $N$ as the sum of two squares. Similarly, it is shown here that the continued fraction expansion of $\sqrt N$ having e
Externí odkaz:
http://arxiv.org/abs/1905.10704
Autor:
Elia, Michele
It is shown that a partition $\mathfrak A\cup \mathfrak B$ of the set $\mathbb F_{p^m}^*=\mathbb F_{p^m}-\{0 \}$, with $|\mathfrak A|=|\mathfrak B|$, is the separation into squares and non squares, if and only if the elements of $\mathfrak A$ and $\m
Externí odkaz:
http://arxiv.org/abs/1903.00169
Publikováno v:
In Applied Mathematics and Computation 15 November 2021 409
Autor:
Elia, Michele, Schipani, Davide
Interesting properties of the partitions of a finite field $\mathbb F_q$ induced by the combination of involutions and trace maps are studied. The special features of involutions of the form $\frac{u}{z}$, $u$ being a fixed element of $\mathbb F_q$,
Externí odkaz:
http://arxiv.org/abs/1609.01212
Autor:
Elia, Michele, Pintore, Federico
It is shown that, under some mild technical conditions, representations of prime numbers by binary quadratic forms can be computed in polynomial complexity by exploiting Schoof's algorithm, which counts the number of $\mathbb F_q$-points of an ellipt
Externí odkaz:
http://arxiv.org/abs/1604.06586
Autor:
Elia, Michele, Gorla, Elisa
The problem of computing the dimension of a left/right ideal in a group algebra F[G] of a finite group G over a field F is considered. The ideal dimension is related to the rank of a matrix originating from a regular left/right representation of G; i
Externí odkaz:
http://arxiv.org/abs/1403.7920