| Title:
|
Finiteness of a class of Rabinowitsch polynomials (English) |
| Author:
|
Schlage-Puchta, Jan-Christoph |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
40 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
259-261 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that there are only finitely many positive integers $m$ such that there is some integer $t$ such that $|n^2+n-m|$ is 1 or a prime for all $n\in [t+1, t+\sqrt{m}]$, thus solving a problem of Byeon and Stark. (English) |
| Keyword:
|
real quadratic fields |
| Keyword:
|
class number |
| Keyword:
|
Rabinowitsch polynomials |
| MSC:
|
11C08 |
| MSC:
|
11R11 |
| MSC:
|
11R29 |
| idZBL:
|
Zbl 1122.11070 |
| idMR:
|
MR2107020 |
| . |
| Date available:
|
2008-06-06T22:43:49Z |
| Last updated:
|
2014-04-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107908 |
| . |
| Reference:
|
[1] Byeon D., Stark H. M.: On the Finiteness of Certain Rabinowitsch Polynomials.J. Number Theory 94 (2002), 177–180. Zbl 1033.11010, MR 1904967, 10.1006/jnth.2001.2729 |
| Reference:
|
[2] Byeon D., Stark H. M.: On the Finiteness of Certain Rabinowitsch Polynomials. II.J. Number Theory 99 (2003), 219–221. Zbl 1033.11010, MR 1957253, 10.1016/S0022-314X(02)00063-X |
| Reference:
|
[3] Heath-Brown D. R.: Zero-free regions for Dirichlet $L$-functions, and the least prime in an arithmetic progression.Proc. London Math. Soc. (3) 64 (1992), 265–338. Zbl 0739.11033, MR 1143227 |
| Reference:
|
[4] Rabinowitsch G.: Eindeutigkeit der Zerlegung in Primzahlfaktoren in quadratischen Zahlkörpern.J. Reine Angew. Mathematik 142 (1913), 153–164. |
| . |
