Divisibility of class numbers of imaginary quadratic fields whose discriminant has only three prime factors

Kostadinka Lapkova

doi:10.1007/s10474-012-0226-3

Divisibility of class numbers of imaginary quadratic fields whose discriminant has only three prime factors

Kostadinka Lapkova^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the existence of infinitely many imaginary quadratic fields whose discriminant has exactly three distinct prime factors and whose class group has an element of a fixed large order. The main tool we use is solving an additive problem via the circle method.

Original language	English
Pages (from-to)	36-63
Number of pages	28
Journal	Acta Mathematica Hungarica
Volume	137
Issue number	1-2
DOIs	https://doi.org/10.1007/s10474-012-0226-3
Publication status	Published - 1 Sept 2012
Externally published	Yes

Keywords

11P55
11R29
circle method
class number
quadratic field

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s10474-012-0226-3

Cite this

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title = "Divisibility of class numbers of imaginary quadratic fields whose discriminant has only three prime factors",

abstract = "We prove the existence of infinitely many imaginary quadratic fields whose discriminant has exactly three distinct prime factors and whose class group has an element of a fixed large order. The main tool we use is solving an additive problem via the circle method.",

keywords = "11P55, 11R29, circle method, class number, quadratic field",

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year = "2012",

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doi = "10.1007/s10474-012-0226-3",

language = "English",

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AB - We prove the existence of infinitely many imaginary quadratic fields whose discriminant has exactly three distinct prime factors and whose class group has an element of a fixed large order. The main tool we use is solving an additive problem via the circle method.

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KW - 11R29

KW - circle method

KW - class number

KW - quadratic field

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DO - 10.1007/s10474-012-0226-3

M3 - Article

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JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1-2

ER -

Divisibility of class numbers of imaginary quadratic fields whose discriminant has only three prime factors

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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