Reference : ON THE (NON-)EQUIVALENCE OF INTEGRAL BINARY QUADRATIC FORMS AND THEIR NEGATIVE FORMS

	Document type :	E-prints/Working papers : First made available on ORBilu
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/42574

Title :	ON THE (NON-)EQUIVALENCE OF INTEGRAL BINARY QUADRATIC FORMS AND THEIR NEGATIVE FORMS
Language :	English
Author, co-author :	Barthel, Jim Jean-Pierre [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
	Müller, Volker [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
Publication date :	Undated
Peer reviewed :	No
Keywords :	[en] Indefinite integral binary quadratic forms ; equivalence classes ; negative forms
Abstract :	[en] Integral binary quadratic forms have been extensively studied in order to compute the class number of real and complex quadratic fields. Many studies restricted the equivalence class of quadratic forms or identified specific forms in order to compute the class number through enumeration of equivalence classes. One often used assumption is that a given form and its negative are equivalent or are synthetically identified. This document presents a concise Lagrangian approach to integral binary quadratic forms, outlines the equivalence classes in its broadest sense and uses it to develop a general condition when a given integral binary quadratic form and its negative are equivalent. Then, the existence of integral binary quadratic forms which are non-equivalent to their negatives is proven and an elementary algorithm to determine the (non-)equivalence of a given form and its negative is outlined.
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/42574
FnR project :	FnR ; FNR10621687 > Sjouke Mauw > SPsquared > Security and Privacy for System Protection > 01/01/2017 > 30/06/2023 > 2016

	File(s) associated to this reference
	Fulltext file(s): File Commentary Version Size Access Limited access Non-EquivalenceOfQuadraticForms.pdf Author preprint 391.76 kB Request a copy Additional material(s): File Commentary Size Access Limited access NegEquivalence.txt 2.24 kB Request a copy

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