Pregled bibliografske jedinice broj: 755247
On the existence of rational Diophantine quintuples with the property D(q)
On the existence of rational Diophantine quintuples with the property D(q) // Explicit Problems in Diophantine Analysis and Geometry
Beč, Austrija, 2013. str. 3-3 (pozvano predavanje, nije recenziran, sažetak, znanstveni)
CROSBI ID: 755247 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
On the existence of rational Diophantine quintuples with the property D(q)
Autori
Dujella, Andrej
Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni
Izvornik
Explicit Problems in Diophantine Analysis and Geometry
/ - , 2013, 3-3
Skup
ESI-Miniworkshop on Explicit Problems in Diophantine Analysis and Geometry
Mjesto i datum
Beč, Austrija, 29.11.2013. - 30.11.2013
Vrsta sudjelovanja
Pozvano predavanje
Vrsta recenzije
Nije recenziran
Ključne riječi
Diophantine quintuples; elliptic curves
Sažetak
We investigate for which rational numbers q there are infinitely many sets consisting of ve nonzero rationals such that the product of any two of them plus q is a square of a rational number. We will present recent joint work with Clemens Fuchs, where we show that there are infinitely many square-free such q, and on assuming the Parity Conjecture for the twists of an explicitly given elliptic curve we derive that the density of such q is at least one half. We will mention some other known results and open problems concerning integer and rational Diophantine m-tuples.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
037-0372781-2821 - Diofantske jednadžbe i eliptičke krivulje (Dujella, Andrej, MZOS ) ( CroRIS)
Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb
Profili:
Andrej Dujella
(autor)
