On pi-adic expansion of singular integers of the p-cyclotomic field
| dc.creator | Queme, Roland | |
| dc.date | 2006-10-31 | |
| dc.date | 2006-11-12 | |
| dc.date.accessioned | 2026-07-07T07:29:40Z | |
| dc.date.available | 2026-07-07T07:29:40Z | |
| dc.description | Let p be an odd prime. Let F_p^* be the no-null part of the finite field of p elements. Let K = Q(zeta) be the p-cyclotomic field and let O_K be the ring of integers of K. Let pi be the prime ideal of K lying over p. An integer B \in O_K is said singular if B^{1/p} not \in K and if B O_K = b^p where b is an ideal of O_K. An integer B \in O_K is said semi-primary if B = beta mod pi^2 where the natural beta is coprime with p. Let sigma be a Q-isomorphism of the field K generating the Galois group Gal(K/Q). When p is irregular, there exists at least one subgroup Gamma of order p of the class group of K annihilated by a polynomial sigma - mu with mu \in F_p^*. We prove the existence, for each Gamma, of singular semi-primary integers B where B O_K= b^p with class Cl(b) \in Gamma and B^{sigma-mu} \in K^p and we describe their pi-adic expansion. This paper is at a strictly elementary level. | |
| dc.description | A correction in proof of lemma 2.2 p. 3 is made | |
| dc.identifier | https://arxiv.org/abs/math/0610968 | |
| dc.identifier | http://arxiv.org/abs/math/0610968 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118201 | |
| dc.subject | Number Theory | |
| dc.subject | 11R18; 11R29 | |
| dc.title | On pi-adic expansion of singular integers of the p-cyclotomic field | |
| dc.type | text |