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Quadratic field
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81	IDEAL CLASS GROUPS OF CYCLOTOMIC NUMBER FIELDS I FRANZ LEMMERMEYER Abstract. Following Hasse’s example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields by carefull Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:03:20 Class field theory Quadratic forms Field theory Conductor Class number formula Field extension Algebraic number field Tensor product of fields Signature Abstract algebra Algebra Algebraic number theory
82	Notes on computing Iwasawa polynomials by PARI/GP Yasushi Mizusawa By referring[removed]and [5], we compute Iwasawa polynomials for the cyclotomic Zp -extensions of imaginary quadratic ﬁelds. √ Preliminaries. Let p b Add to Reading List Source URL: mizusawa.web.nitech.ac.jp Language: English - Date: 2013-07-31 13:24:55 Mathematics Operator theory Ordinary differential equations Field theory Coding theory Spectral theory of ordinary differential equations Λ-ring Abstract algebra Spectral theory Algebra
83	IDEAL CLASS GROUPS OF CYCLOTOMIC NUMBER FIELDS II FRANZ LEMMERMEYER Abstract. We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:03:22 Hilbert class field Cubic field Tensor product of fields Galois module Kummer theory Conductor Field extension Ideal class group Quadratic field Abstract algebra Algebra Algebraic number theory
84	CONSTRUCTION OF HILBERT 2-CLASS FIELDS FRANZ LEMMERMEYER Abstract. Let F be a number field with odd class number, and suppose that k/F is a quadratic extension. We will deal with the problem of constructing parts of the Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:03:18 Quadratic field Hilbert class field Algebraic number field Ideal class group Splitting of prime ideals in Galois extensions Discriminant Reciprocity law Quaternion algebra Field extension Abstract algebra Algebra Algebraic number theory
85	THE DEVELOPMENT OF THE PRINCIPAL GENUS THEOREM FRANZ LEMMERMEYER Introduction Genus theory belongs to algebraic number theory and, in very broad terms, deals with the part of the ideal class group of a number field that Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:19:38 Algebraic number theory Quadratic forms Modular arithmetic Number theory Quadratic residue Binary quadratic form Quadratic reciprocity Ideal class group Algebraic number field Abstract algebra Mathematics Algebra
86	SELMER GROUPS AND QUADRATIC RECIPROCITY FRANZ LEMMERMEYER Abstract. In this article we study the 2-Selmer groups of number fields F as well as some related groups, and present connections to the quadratic reciprocity law Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2005-03-14 17:20:19 Algebraic number theory Modular arithmetic Quadratic residue Class field theory Quadratic reciprocity Reciprocity law Selmer group Algebraic number field Artin reciprocity law Abstract algebra Mathematics Number theory
87	THE 4-CLASS GROUP OF REAL QUADRATIC NUMBER FIELDS FRANZ LEMMERMEYER Abstract. In this paper we give an elementary proof of results on the structure of 4-class groups of real quadratic number fields originally due to A. S Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:03:59 Mathematics Quadratic field Discriminant Quaternion algebra Splitting of prime ideals in Galois extensions Algebraic number field Quadratic reciprocity Ideal class group Discriminant of an algebraic number field Abstract algebra Algebraic number theory Algebra
88	A Note on P´epin’s counter examples to the Hasse principle for curves of genus 1 Franz Lemmermeyer Bilkent University[removed]Bilkent, Ankara September 11, 2003 Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:04:04 Algebraic number theory Modular arithmetic Field theory Analytic number theory Elliptic curve Quadratic reciprocity Infinite descent Algebraic number field P-adic number Mathematics Abstract algebra Number theory
89	ON 2-CLASS FIELD TOWERS OF SOME IMAGINARY QUADRATIC NUMBER FIELDS FRANZ LEMMERMEYER Abstract. We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2, 2, 2) whose Hilbert 2-cla Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:03:05 Class field theory Field theory Artin reciprocity law Hilbert class field Class number formula Field extension Conductor Algebraic number field Normal extension Abstract algebra Algebra Algebraic number theory
90	Philosophers’ Imprint volume 000, no. 00 october 23, 2014 Add to Reading List Source URL: pincock-yilmazer.com Language: English - Date: 2014-10-26 22:33:57 Group theory Galois theory Polynomials Equations Évariste Galois Quintic function Galois group Field Quadratic equation Abstract algebra Algebra Field theory

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