Deshouillers, J.-M. ; Gun, S. ; Sivaraman, J. (2020) On Euclidean ideal classes in certain Abelian extensions Mathematische Zeitschrift, 296 (1-2). pp. 847-859. ISSN 0025-5874
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Official URL: http://doi.org/10.1007/s00209-019-02434-2
Related URL: http://dx.doi.org/10.1007/s00209-019-02434-2
Abstract
In this article, we show that certain abelian extensions K with unit rank greater than or equal to three have cyclic class group if and only if it has a Euclidean ideal class. This result improves an earlier result of Murty and Graves. One can improve this result up to unit rank 2 if one assumes the Elliott and Halberstam conjecture (see Conjecture 1 in preliminaries). These results are known under generalized Riemann hypothesis by the work of Lenstra (J Lond Math Soc 10:457–465) [see also Weinberger (Proc Symp Pure Math 24:321–332)].
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer Nature. |
| Keywords: | Euclidean Ideal Classes; Galois Theory; Hilbert Class Fields; Brun’s Sieve; Bombieri–Vinogradov Theorem; Linear Sieve. |
| ID Code: | 118022 |
| Deposited On: | 11 May 2021 06:52 |
| Last Modified: | 11 May 2021 06:52 |
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