scholarly journals Continued fractions and class number two

2001 ◽  
Vol 27 (9) ◽  
pp. 565-571
Author(s):  
Richard A. Mollin
Keyword(s):  
Continued Fractions ◽  
Class Number ◽  
Quadratic Field ◽  
Ideal Theory ◽  
Quadratic Polynomial ◽  
Quadratic Fields ◽  
Real Quadratic Field ◽  
Real Quadratic Fields ◽  
New Class ◽  
Real Quadratic

We use the theory of continued fractions in conjunction with ideal theory (often called the infrastructure) in real quadratic fields to give new class number 2 criteria and link this to a canonical norm-induced quadratic polynomial. By doing so, this provides a real quadratic field analogue of the well-known result by Hendy (1974) for complex quadratic fields. We illustrate with several examples.

Utopophobia

2019 ◽  
Author(s):  
David Estlund
Keyword(s):  
Political Philosophy ◽  
Social Justice ◽  
Political Thought ◽  
Political Action ◽  
Ideal Theory ◽  
Theory Of Justice ◽  
Sound Theory ◽  
Theory Versus ◽  
History Of ◽  
Practical Guidance

Throughout the history of political philosophy and politics, there has been continual debate about the roles of idealism versus realism. For contemporary political philosophy, this debate manifests in notions of ideal theory versus nonideal theory. Nonideal thinkers shift their focus from theorizing about full social justice, asking instead which feasible institutional and political changes would make a society more just. Ideal thinkers, on the other hand, question whether full justice is a standard that any society is likely ever to satisfy. And, if social justice is unrealistic, are attempts to understand it without value or importance, and merely utopian? This book argues against thinking that justice must be realistic, or that understanding justice is only valuable if it can be realized. The book does not offer a particular theory of justice, nor does it assert that justice is indeed unrealizable—only that it could be, and this possibility upsets common ways of proceeding in political thought. The book's author engages critically with important strands in traditional and contemporary political philosophy that assume a sound theory of justice has the overriding, defining task of contributing practical guidance toward greater social justice. Along the way, it counters several tempting perspectives, including the view that inquiry in political philosophy could have significant value only as a guide to practical political action, and that understanding true justice would necessarily have practical value, at least as an ideal arrangement to be approximated. Demonstrating that unrealistic standards of justice can be both sound and valuable to understand, the book stands as a trenchant defense of ideal theory in political philosophy.

The Role of Ideal Theory

2018 ◽  
Author(s):  
Christie Hartley
Keyword(s):  
Ideal Theory ◽  
Racial Minorities ◽  
Gender Inequalities ◽  
Liberal Society ◽  
Social Categories ◽  
Ideal Society ◽  
Gender And Race ◽  
Theories Of Justice ◽  
Comprehensive Doctrines

This chapter discusses whether political liberalism’s commitment to ideal theory makes it ill-suited for theorizing about justice for socially subordinated groups such as women and racial minorities. It is shown that political liberalism’s commitment to ideal theory does not entail assuming away race or gender as social categories that give rise to concerns about justice. Even within a politically liberal well-ordered (ideal) society racial or gender inequalities may arise due to the role that beliefs about race or gender play in some persons’ comprehensive doctrines. Furthermore, it is argued that theories of justice developed for a well-ordered politically liberal society provide important guidance for correcting injustices on the basis of gender and race in nonideal societies.

Introduction

2017 ◽  
Author(s):  
Clare Chambers
Keyword(s):  
Ideal Theory ◽  
Free State ◽  
Regulatory Structure ◽  
Intended Audience ◽  
Political Commitments

The introduction sets out the arguments of Against Marriage: An Egalitarian Defence of the Marriage-Free State. It starts with the question of the intended audience for the book, discussing the implications for those with both personal and political commitments. It outlines the negative thesis against marriage offered in Part One, and the positive thesis in favour of an alternative regulatory structure in Part Two. It summarizes the contents of each chapter. It also includes a discussion of the book’s location within ideal and non-ideal theory.

Humanitarian Intervention and Non-Ideal Theory

2018 ◽  
Author(s):  
Ramon Das
Keyword(s):  
Human Rights ◽  
Civil War ◽  
Humanitarian Intervention ◽  
Ideal Theory ◽  
Military Power ◽  
Moral Integrity ◽  
Philosophical Debate ◽  
Human Rights Abuses ◽  
Target State ◽  
Target States

This chapter argues that the philosophical debate around humanitarian intervention would be improved if it were less ‘ideal-theoretic’. It identifies two ideal-theoretic assumptions. One, in target states where humanitarian intervention is being considered, there are two distinct and easily identified groups: ‘bad guys’ committing serious human rights abuses, and innocent civilians against whom the abuses are being committed. Two, external to the target state in question, there are suitably qualified ‘good guys’—prospective interveners who possess both the requisite military power and moral integrity. If the assumptions hold, the prospects for successful humanitarian intervention are much greater. As a contrast, some possible non-ideal assumptions are that (i) there are many bad guys in a civil war, and (ii) the good guy intervener is itself supporting some of the bad guys. If these non-ideal assumptions hold, prospects for successful humanitarian intervention are small.

scholarly journals EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES

2020 ◽  
pp. 1-36
Author(s):  
Bart Michels
Keyword(s):  
Lower Bound ◽  
Closed Geodesic ◽  
Extreme Values ◽  
Theta Series ◽  
Hyperbolic Surface ◽  
Quadratic Fields ◽  
Maass Forms ◽  
Real Quadratic Fields ◽  
Central Values ◽  
Real Quadratic

Abstract Given a closed geodesic on a compact arithmetic hyperbolic surface, we show the existence of a sequence of Laplacian eigenfunctions whose integrals along the geodesic exhibit nontrivial growth. Via Waldspurger’s formula we deduce a lower bound for central values of Rankin-Selberg L-functions of Maass forms times theta series associated to real quadratic fields.

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