A positive proportion of locally soluble quartic Thue equations are globally insoluble

Shabnam Akhtari

doi:10.1017/S0305004121000554

A positive proportion of locally soluble quartic Thue equations are globally insoluble

Shabnam Akhtari

Mathematics

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

1 Scopus citations

Abstract

For any fixed nonzero integer h, we show that a positive proportion of integral binary quartic forms F do locally everywhere represent h, but do not globally represent h. We order classes of integral binary quartic forms by the two generators of their ring of -invariants, classically denoted by I and J.

Original language	English (US)
Pages (from-to)	333-348
Number of pages	16
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	173
Issue number	2
DOIs	https://doi.org/10.1017/S0305004121000554
State	Published - Sep 5 2022

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/S0305004121000554

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title = "A positive proportion of locally soluble quartic Thue equations are globally insoluble",

abstract = "For any fixed nonzero integer h, we show that a positive proportion of integral binary quartic forms F do locally everywhere represent h, but do not globally represent h. We order classes of integral binary quartic forms by the two generators of their ring of -invariants, classically denoted by I and J.",

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AB - For any fixed nonzero integer h, we show that a positive proportion of integral binary quartic forms F do locally everywhere represent h, but do not globally represent h. We order classes of integral binary quartic forms by the two generators of their ring of -invariants, classically denoted by I and J.

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A positive proportion of locally soluble quartic Thue equations are globally insoluble

Abstract

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