| Title:
|
On the arithmetic of the hyperelliptic curve $y^2=x^n+a$ (English) |
| Author:
|
Aktaş, Kevser |
| Author:
|
Şenay, Hasan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
35-40 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the arithmetic properties of hyperelliptic curves given by the affine equation $y^2=x^n+a$ by exploiting the structure of the automorphism groups. We show that these curves satisfy Lang's conjecture about the covering radius (for some special covering maps). (English) |
| Keyword:
|
hyperelliptic curve |
| Keyword:
|
Lang's conjecture |
| MSC:
|
11G30 |
| MSC:
|
14H25 |
| idZBL:
|
Zbl 06587870 |
| idMR:
|
MR3483219 |
| DOI:
|
10.1007/s10587-016-0236-3 |
| . |
| Date available:
|
2016-04-07T14:49:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144869 |
| . |
| Reference:
|
[1] Birkenhake, C., Lange, H.: Complex Abelian Varieties.Grundlehren der Mathematischen Wissenschaften 302 Springer, Berlin (2004). Zbl 1056.14063, MR 2062673 |
| Reference:
|
[2] Lang, S.: Hyperbolic and Diophantine analysis.Bull. Am. Math. Soc., New Ser. 14 (1986), 159-205. MR 0828820, 10.1090/S0273-0979-1986-15426-1 |
| Reference:
|
[3] Wolfart, J.: The `Obvious' part of Belyi's theorem and Riemann surfaces with many automorphisms.Geometric Galois Actions. 1. Around Grothendieck's "Esquisse d'un Programme" L. Schneps et al. Proc. Conf. on geometry and arithmetic of moduli spaces, Luminy, France, 1995. Lond. Math. Soc. Lect. Note Ser. 242 Cambridge University Press, Cambridge (1997), 97-112. MR 1483112 |
| Reference:
|
[4] Wolfart, J.: Taylorentwicklungen automorpher Formen und ein Transzendenzproblem aus der Uniformisierungstheorie.Abh. Math. Semin. Univ. Hamb. 54 German (1984), 25-33. MR 0780235, 10.1007/BF02941437 |
| Reference:
|
[5] Wolfart, J., Wüstholz, G.: Der Überlagerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen.Math. Ann. 273 (1985), German 1-15. MR 0814192, 10.1007/BF01455911 |
| . |
