Zobrazeno 1 - 10
of 249
pro vyhledávání: '"Fundamental unit (number theory)"'
Autor:
Jigu Kim, Dongho Byeon
Publikováno v:
Journal of Number Theory. 231:1-47
Let d > 0 be a fundamental discriminant of a real quadratic field. Let h ( d ) be the class number and e d the fundamental unit of the real quadratic field Q ( d ) . In this paper, we prove that if there is an elliptic curve E over Q whose Hasse-Weil
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c6a46cbb6ac93b07c80725b6c116fb63
https://doi.org/10.1016/j.jnt.2020.11.015
https://doi.org/10.1016/j.jnt.2020.11.015
Autor:
Sevcan Isikay, Ayten Pekin
Publikováno v:
International Journal of Number Theory. 18:473-484
Let [Formula: see text] be a positive square-free integer and [Formula: see text] be the fundamental unit of the real quadratic field [Formula: see text]. The Ankeny–Artin–Chowla (AAC) conjecture asserts that [Formula: see text] (mod [Formula: se
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1656a0b7325f4ba7ae79fd45ad8a1688
https://doi.org/10.1142/s1793042122500270
https://doi.org/10.1142/s1793042122500270
Publikováno v:
TURKISH JOURNAL OF MATHEMATICS. 45:1689-1704
Let $p$ be a prime number such that $p=2$ or $p\equiv 1\pmod 4$. Let $\varepsilon_p$ denote the fundamental unit of $\mathbb{Q}(\sqrt{p})$ and let $a$ be a positive square-free integer. The main aim of this paper is to determine explicitly the Hilber
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::42dc5cc8544eb4fef85d9cdbe8b50ce4
https://doi.org/10.3906/mat-2101-120
https://doi.org/10.3906/mat-2101-120
Autor:
Jianing Li
Publikováno v:
Asian Journal of Mathematics. 25:177-182
In this paper, we prove a result on the $2$-adic logarithm of the fundamental unit of the field $\mathbb{Q}(\sqrt[4]{-q}) $, where $q\equiv 3\bmod 4$ is a prime. When $q\equiv 15\bmod 16$, this result confirms a speculation of Coates-Li and has conse
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::286c2e08546dee1cdf16d9eb6ee38afe
https://doi.org/10.4310/ajm.2021.v25.n2.a1
https://doi.org/10.4310/ajm.2021.v25.n2.a1
Autor:
Joachim Petit
Publikováno v:
International Mathematics Research Notices. 2022:7056-7099
We investigate the number of curves having a rational point of almost minimal height in the family of quadratic twists of a given elliptic curve. This problem takes its origin in the work of Hooley, who asked this question in the setting of real quad
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::59d319fdc4c1b3827ee3882899f04992
https://doi.org/10.1093/imrn/rnaa326
https://doi.org/10.1093/imrn/rnaa326
Autor:
P. G. Walsh
Publikováno v:
Mathematics of Computation. 90:2503-2505
In this short note, we identify an error made in an earlier paper [Math. Comp. 68 (1999), no. 225, pp. 385–388] on simultaneous Pell equations, provide a revised statement of the main results contained therein, and show how this modification lends
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bfdb3731b7c8453c1547de9e088a92e3
https://doi.org/10.1090/mcom/3677
https://doi.org/10.1090/mcom/3677
Autor:
G. V. Fedorov
Publikováno v:
Doklady Mathematics. 102:513-517
In the classical case, the connection between the periodicity of the continued fraction of $$\sqrt f $$ and the existence of a fundamental unit of the corresponding hyperelliptic field $$\mathcal{L} = K(x)(\sqrt f )$$ , where K is a field of characte
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0bd7d8e77f66ae87449033032cc59d1f
https://doi.org/10.1134/s1064562420060101
https://doi.org/10.1134/s1064562420060101
Publikováno v:
The Journal of Physical Chemistry C. 124:24408-24419
As a fundamental unit of molecule-based electronics, a molecular rectifier is one of the most widely studied molecular devices, of which the ideal current–voltage (I–V) characteristics based on a t...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::65c450c682bc96b60e6d431da4806fe7
https://doi.org/10.1021/acs.jpcc.0c06647
https://doi.org/10.1021/acs.jpcc.0c06647
Publikováno v:
Mechanics Based Design of Structures and Machines. 50:3452-3474
In this article, five fundamental unit cells namely BCC, hexagonal packing, rhombicuboctahedron, diamond, and truncated octahedron, for which there was a lack of accurate analytical yield stress re...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::04e7e19c39f45d6aff3340f369517777
https://doi.org/10.1080/15397734.2020.1807363
https://doi.org/10.1080/15397734.2020.1807363
Autor:
Ingemar Bengtsson
Publikováno v:
Quantum Information and Computation. 20:400-417
In complex vector spaces maximal sets of equiangular lines, known as SICs, are related to real quadratic number fields in a dimension dependent way. If the dimension is of the form $n^2+3$ the base field has a fundamental unit of negative norm, and t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::adbea4f03b1a539e80d2c9fe9fb521f0
https://doi.org/10.26421/qic20.5-6-3
https://doi.org/10.26421/qic20.5-6-3