Counting ideals in ray classes

被引：1
|
作者：
Gun, Sanoli [1 ]
Ramare, Olivier [2 ]
Sivaraman, Jyothsnaa [3 ]
机构：
[1] Homi Bhabha Natl Inst, Inst Math Sci, CIT Campus, Chennai 600113, Tamil Nadu, India
[2] Aix Marseille Univ, CNRS, Inst Math Marseille, UMR 7373, Site Sud,Campus Luminy,Case 907, F-13288 Marseille 9, France
[3] Chennai Math Inst, H1,SIPCOT IT Pk, Siruseri 603103, Kelambakkam, India
来源：
JOURNAL OF NUMBER THEORY | 2023年 / 243卷
关键词：
Ray class group; Korkin-Zolotarev basis; Counting ideals;
D O I：
10.1016/j.jnt.2022.08.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let K be a number field and q an integral ideal in OK. A result of Tatuzawa [11] from 1973, computes the asymptotic (with an error term) for the number of ideals with norm at most x in a class of the narrow ray class group of K modulo q. This result bounds the error term with a constant whose dependence on q is explicit but dependence on K is not explicit. The aim of this paper is to prove this asymptotic with a fully explicit bound for the error term.(c) 2022 Elsevier Inc. All rights reserved.
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收藏
页码：13 / 37
页数：25
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