Reciprocity Laws

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Reciprocity Laws From Euler to Eisenstein

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Author by : Franz Lemmermeyer
Languange Used : English, France, Spanish, Italia and chinese
Page : 492
Isbn : 3662128934
Identifier : 9783662128930
Release : 2013-03-14
Publisher by : Springer Science & Business Media
Category : Mathematics
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Description : Read Now Reciprocity Laws by Franz Lemmermeyer and you can download with pub, pdf, txt, doc, and more file format with free account. this book covers the development of reciprocity laws, starting from conjectures of euler and discussing the contributions of legendre, gauss, dirichlet, jacobi, and eisenstein. readers knowledgeable in basic algebraic number theory and galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and eisensteins reciprocity law. an extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.

The Quadratic Reciprocity Law A Collection of Classical Proofs

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Author by : Oswald Baumgart
Languange Used : English, France, Spanish, Italia and chinese
Page : 172
Isbn : 3319162837
Identifier : 9783319162836
Release : 2015-05-27
Publisher by : Birkhäuser
Category : Mathematics
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Description : Read Now The Quadratic Reciprocity Law by Oswald Baumgart and you can download with pub, pdf, txt, doc, and more file format with free account. this book is the english translation of baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische reciprocitätsgesetz. eine vergleichende darstellung der beweise”), first published in 1885. it is divided into two parts. the first part presents a very brief history of the development of number theory up to legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. the second part highlights baumgart’s comparisons of the principles behind these proofs. a current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. this book will appeal to all readers interested in elementary number theory and the history of number theory.

Reciprocity in International Law Its impact and function

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Author by : Shahrad Nasrolahi Fard
Languange Used : English, France, Spanish, Italia and chinese
Page : 178
Isbn : 1317312198
Identifier : 9781317312192
Release : 2015-12-22
Publisher by : Routledge
Category : Law
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Description : Read Now Reciprocity In International Law by Shahrad Nasrolahi Fard and you can download with pub, pdf, txt, doc, and more file format with free account. in international relations, reciprocity describes an environment in which states support one another for short- or long-term advantage through the balancing of rights, duties and interests. this book examines reciprocity in the context of international law. it considers the role reciprocity plays in the creation and development of international law as well as in the interpretation and application of international law. the book illuminates the reciprocal framework of international law and international relations by examining the role reciprocity plays in different types of states’ obligations, including bilateral, bilateralisable multilateral, non-bilateralisable multilateral and obligations erga omnes. the book examines how reciprocity is intertwined with the principle of equality, as the rights and obligations of states are equal irrespective of size and economic or military strength, and the beneficial effects of reciprocity in creating stability and cooperation amongst states.

p-Adic Automorphic Forms on Shimura Varieties

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Author by : Haruzo Hida
Languange Used : English, France, Spanish, Italia and chinese
Page : 390
Isbn : 9780387207117
Identifier : 0387207112
Release : 2004-05-10
Publisher by : Springer Science & Business Media
Category : Mathematics
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Description : Read Now P Adic Automorphic Forms On Shimura Varieties by Haruzo Hida and you can download with pub, pdf, txt, doc, and more file format with free account. this book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1. an elementary construction of shimura varieties as moduli of abelian schemes. 2. p-adic deformation theory of automorphic forms on shimura varieties. 3. a simple proof of irreducibility of the generalized igusa tower over the shimura variety. the book starts with a detailed study of elliptic and hilbert modular forms and reaches to the forefront of research of shimura varieties associated with general classical groups. the method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. the area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. specifically, the use of p-adic elliptic and hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of fermat's last theorem and the shimura-taniyama conjecture by a. wiles and others). haruzo hida is professor of mathematics at university of california, los angeles. his previous books include modular forms and galois cohomology (cambridge university press 2000) and geometric modular forms and elliptic curves (world scientific publishing company 2000).

The Fourier-Analytic Proof of Quadratic Reciprocity

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Author by : Michael C. Berg
Languange Used : English, France, Spanish, Italia and chinese
Page : 118
Isbn : 1118031199
Identifier : 9781118031193
Release : 2011-09-30
Publisher by : John Wiley & Sons
Category : Mathematics
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Description : Read Now The Fourier Analytic Proof Of Quadratic Reciprocity by Michael C. Berg and you can download with pub, pdf, txt, doc, and more file format with free account. a unique synthesis of the three existing fourier-analytictreatments of quadratic reciprocity. the relative quadratic case was first settled by hecke in 1923,then recast by weil in 1964 into the language of unitary grouprepresentations. the analytic proof of the general n-th order caseis still an open problem today, going back to the end of hecke'sfamous treatise of 1923. the fourier-analytic proof of quadraticreciprocity provides number theorists interested in analyticmethods applied to reciprocity laws with a unique opportunity toexplore the works of hecke, weil, and kubota. this work brings together for the first time in a single volume thethree existing formulations of the fourier-analytic proof ofquadratic reciprocity. it shows how weil's groundbreakingrepresentation-theoretic treatment is in fact equivalent to hecke'sclassical approach, then goes a step further, presenting kubota'salgebraic reformulation of the hecke-weil proof. extensivecommutative diagrams for comparing the weil and kubotaarchitectures are also featured. the author clearly demonstrates the value of the analytic approach,incorporating some of the most powerful tools of modern numbertheory, including adèles, metaplectric groups, andrepresentations. finally, he points out that the critical commonfactor among the three proofs is poisson summation, whosegeneralization may ultimately provide the resolution for hecke'sopen problem.

Gun Laws by State 2018 Edition Reciprocity and Gun Laws Quick Reference Guide

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Author by : Bryan L Ciyou Esq
Languange Used : English, France, Spanish, Italia and chinese
Page : 233
Isbn : 9781946208767
Identifier : 1946208760
Release : 2017-11-07
Publisher by : Vervante
Category :
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Description : Read Now Gun Laws By State 2018 Edition by Bryan L Ciyou Esq and you can download with pub, pdf, txt, doc, and more file format with free account. preparing you for the time when "what if" becomes "what is." written by a prominent gun law author, and nationally recognized gun law attorney. 490 pages. covers reciprocal carry of 50 states, constitutional & federal law, use of force, criminal provisions, civil & criminal liability, preemption, federal property & interstate transportation & hr 218.

A Classical Introduction to Modern Number Theory

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Author by : Kenneth Ireland
Languange Used : English, France, Spanish, Italia and chinese
Page : 389
Isbn : 9780387973296
Identifier : 038797329X
Release : 1990-09-07
Publisher by : Springer Science & Business Media
Category : Mathematics
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Description : Read Now A Classical Introduction To Modern Number Theory by Kenneth Ireland and you can download with pub, pdf, txt, doc, and more file format with free account. bridging the gap between elementary number theory and the systematic study of advanced topics, a classical introduction to modern number theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. an extensive bibliography and many challenging exercises are also included. this second edition has been corrected and contains two new chapters which provide a complete proof of the mordell-weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.

Quadratic Irrationals An Introduction to Classical Number Theory

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Author by : Franz Halter-Koch
Languange Used : English, France, Spanish, Italia and chinese
Page : 431
Isbn : 1466591846
Identifier : 9781466591844
Release : 2013-06-17
Publisher by : CRC Press
Category : Mathematics
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Description : Read Now Quadratic Irrationals by Franz Halter-Koch and you can download with pub, pdf, txt, doc, and more file format with free account. quadratic irrationals: an introduction to classical number theory gives a unified treatment of the classical theory of quadratic irrationals. presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups. the book highlights the connection between gauss’s theory of binary forms and the arithmetic of quadratic orders. it collects essential results of the theory that have previously been difficult to access and scattered in the literature, including binary quadratic diophantine equations and explicit continued fractions, biquadratic class group characters, the divisibility of class numbers by 16, f. mertens’ proof of gauss’s duplication theorem, and a theory of binary quadratic forms that departs from the restriction to fundamental discriminants. the book also proves dirichlet’s theorem on primes in arithmetic progressions, covers dirichlet’s class number formula, and shows that every primitive binary quadratic form represents infinitely many primes. the necessary fundamentals on algebra and elementary number theory are given in an appendix. research on number theory has produced a wealth of interesting and beautiful results yet topics are strewn throughout the literature, the notation is far from being standardized, and a unifying approach to the different aspects is lacking. covering both classical and recent results, this book unifies the theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational.

An explicit 2n-th reciprocity law

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Author by : Charles Helou
Languange Used : English, France, Spanish, Italia and chinese
Page : 178
Isbn :
Identifier : CORNELL:31924000084941
Release : 1984
Publisher by : no defined
Category : Reciprocity theorems
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The Counterinsurgent's Constitution Law in the Age of Small Wars

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Author by : Ganesh Sitaraman
Languange Used : English, France, Spanish, Italia and chinese
Page : 352
Isbn : 0199986908
Identifier : 9780199986903
Release : 2012-12-01
Publisher by : Oxford University Press
Category : Law
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Description : Read Now The Counterinsurgent S Constitution by Ganesh Sitaraman and you can download with pub, pdf, txt, doc, and more file format with free account. since the "surge" in iraq in 2006, counterinsurgency effectively became america's dominant approach for fighting wars. yet many of the major controversies and debates surrounding counterinsurgency have turned not on military questions but on legal ones: who can the military attack with drones? is the occupation of iraq legitimate? what tradeoffs should the military make between self-protection and civilian casualties? what is the right framework for negotiating with the taliban? how can we build the rule of law in afghanistan? the counterinsurgent's constitution tackles this wide range of legal issues from the vantage point of counterinsurgency strategy. ganesh sitaraman explains why law matters in counterinsurgency: how it operates on the ground and how law and counterinsurgency strategy can be better integrated. counterinsurgency, sitaraman notes, focuses on winning over the population, providing essential services, building political and legal institutions, and fostering economic development. so, unlike in conventional war, where law places humanitarian restraints on combat, law and counterinsurgency are well aligned and reinforce one another. indeed, following the law and building the rule of law is not just the right thing to do, it is strategically beneficial. moreover, reconciliation with enemies can both help to end the conflict and preserve the possibility of justice for war crimes. following the rule of law is an important element of success. the first book on law and counterinsurgency strategy, the counterinsurgent's constitution seamlessly integrates law and military strategy to illuminate some of the most pressing issues in warfare and the transition from war to peace. its lessons also apply to conflicts in libya and other hot-spots in the middle east.

Emil Artin and Helmut Hasse The Correspondence 1923-1958

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Author by : Günther Frei
Languange Used : English, France, Spanish, Italia and chinese
Page : 484
Isbn : 3034807155
Identifier : 9783034807159
Release : 2014-01-16
Publisher by : Springer Science & Business Media
Category : Mathematics
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Description : Read Now Emil Artin And Helmut Hasse by Günther Frei and you can download with pub, pdf, txt, doc, and more file format with free account. this volume consists of the english translations of the letters exchanged between emil artin to helmut hasse written from 1921 until 1958. the letters are accompanied by extensive comments explaining the mathematical background and giving the information needed for understanding these letters. most letters deal with class field theory and shed a light on the birth of one of its most profound results: artin's reciprocity law.

A dual reciprocity map for local fields

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Author by : Thomas Madison Lamm
Languange Used : English, France, Spanish, Italia and chinese
Page : 80
Isbn :
Identifier : CORNELL:31924001408925
Release : 1976
Publisher by : no defined
Category : Mathematics
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Description : Read Now A Dual Reciprocity Map For Local Fields by Thomas Madison Lamm and you can download with pub, pdf, txt, doc, and more file format with free account.