Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Pedro Berrizbeitia"'
Publikováno v:
Qualitative Theory of Dynamical Systems. 20
In the present article we study the periodic structure of a class of maps on the n-dimensional torus such that the eigenvalues of the induced map on the first homology are dilations of roots of unity. This family of maps shares some properties with t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::47fbccdb5a7fb8ec8bd4d4b1c3246ba7
https://doi.org/10.1007/s12346-021-00453-1
https://doi.org/10.1007/s12346-021-00453-1
Publikováno v:
Topology and its Applications. 235:428-444
We provide a general formula and give an explicit expression of the Lefschetz zeta function for any quasi-unipotent map on the space X = S l × ⋯ × ︸ n − times S l , with l > 1 . Among the quasi-unipotent maps are Morse–Smale diffeomorphisms
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::92498e29d9642e8412d4c35221a6f724
https://doi.org/10.1016/j.topol.2017.12.023
https://doi.org/10.1016/j.topol.2017.12.023
Publikováno v:
Journal of Number Theory. 175:134-139
We prove that if { A n } n ≥ 0 is any Lucas sequence and p is any prime, then 4 A p admits a representation by one of two quadratic forms according to the residue class of p modulo 4.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::152ea3253bf88de428119739712e27ce
https://doi.org/10.1016/j.jnt.2016.11.021
https://doi.org/10.1016/j.jnt.2016.11.021
Publikováno v:
Topology and its Applications. 210:246-262
We provide a general formula and give an explicit expression of the Lefschetz zeta function for any quasi-unipotent map on the n -dimensional torus. The Lefschetz zeta function is used to characterize the minimal set of Lefschetz periods for Morse–
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::31b2e4cd1c8ec6c0fba942927088fab7
https://doi.org/10.1016/j.topol.2016.07.020
https://doi.org/10.1016/j.topol.2016.07.020
Publikováno v:
International Journal of Number Theory. 11:185-191
In this paper, we show that if p ≡ 1 ( mod 4) is prime, then Fp admits a representation of the form u2 + pv2 for some integers u and v, where Fn is the nth Fibonacci number.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dc295328926976d5bf912acbd3a58b3f
https://doi.org/10.1142/s1793042115500116
https://doi.org/10.1142/s1793042115500116
Autor:
Víctor F. Sirvent, Pedro Berrizbeitia
Publikováno v:
Journal of Difference Equations and Applications. 20:961-972
We compute the Lefschetz zeta function for quasi-unipotent maps on the n-dimensional torus, using arithmetical properties of the number n. In particular we compute the Lefschetz zeta function for quasi-unipotent maps, such that the characteristic pol
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::98439e8d67db2317131f97c8ec850339
https://doi.org/10.1080/10236198.2013.872637
https://doi.org/10.1080/10236198.2013.872637
Autor:
Florian Luca, Pedro Berrizbeitia
Publikováno v:
Journal of Number Theory. 131(4):605-617
In this paper, we confirm a conjecture of Bergelson and Shapiro concerning subgroups of finite index in multiplicative groups of fields which have maximal additive dimension. We also show that the natural extension of subgroups G p of prime index p i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f9af840120c3e0a48729688029bea878
Autor:
Pedro Berrizbeitia, Boris Iskra
Publikováno v:
Mathematics of Computation. 79:1779-1791
The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas-Lehrner test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a77c3845e239f833514e7775440d8bf4
https://doi.org/10.1090/s0025-5718-10-02324-0
https://doi.org/10.1090/s0025-5718-10-02324-0
Autor:
Aurora Olivieri, Pedro Berrizbeitia
Publikováno v:
Proceedings of the American Mathematical Society. 136:3095-3104
For any integer r r we show that the notion of ω \omega -prime to base a a introduced by Berrizbeitia and Berry, 2000, leads to a primality test for numbers n n congruent to 1 1 modulo r r , which runs in polynomial time assuming the Extended Rieman
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b2b369a337fc969d03caa3e261b9aec9
https://doi.org/10.1090/s0002-9939-08-09303-9
https://doi.org/10.1090/s0002-9939-08-09303-9
Publikováno v:
Discrete Mathematics. 282:239-243
For n∈N let pk(n) be the number of induced k-cycles in the Cayley graph Cay (Zn,Un), where Zn is the ring of integers modn and Un=Zn∗ is the group of units modn. Our main result is: Given r∈N there is a number m(r), depending only on r, with rl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::decb5cab412aacadd4889460a75df676
https://doi.org/10.1016/j.disc.2003.11.013
https://doi.org/10.1016/j.disc.2003.11.013