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Quadratic reciprocity
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21	Beitr¨age zur Algebra und Geometrie Contributions to Algebra and Geometry Volume[removed]), No. 1, [removed]Belyi’s Theorem Revisited Bernhard K¨ Add to Reading List Source URL: www.kurims.kyoto-u.ac.jp Language: English - Date: 2004-01-25 09:20:12 Group theory Covering space Homotopy theory Elliptic curve Automorphism Field extension Finite field Orbifold Proofs of quadratic reciprocity Abstract algebra Mathematics Algebra
22	ON A THEOREM OF AUBRY-THUE ALFRED BRAUER AND R. L. REYNOLDS 1. Introduction. In 1913 L. Aubry [1] proved the following theorem: Add to Reading List Source URL: www.math.uga.edu Language: English - Date: 2011-09-25 15:53:25 Modular arithmetic Quadratic residue Linear congruence theorem Algebraic number field Prime number Coprime Quadratic reciprocity Wieferich prime Abstract algebra Mathematics Number theory
23	RATIONAL QUARTIC RECIPROCITY FRANZ LEMMERMEYER Abstract. We provide a simple proof of the general rational quartic reciprocity law due to Williams, Hardy and Friesen. In 1985, K. S. Williams, K. Hardy and C. Friesen [11 Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:03:07 Modular arithmetic Algebraic number theory Quadratic residue Quartic reciprocity Reciprocity law Quadratic reciprocity Legendre symbol Prime number Reciprocity Abstract algebra Number theory Mathematics
24	EULER’S TRICK AND SECOND 2-DESCENTS ¨ ¨ OZT ¨ ¨ UN ¨ Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2005-05-14 16:56:15 Algebraic number theory Modular arithmetic Greatest common divisor Quadratic reciprocity Unique factorization domain Algebraic number field Euclidean algorithm Mathematics Abstract algebra Number theory
25	SOME FAMILIES OF NON-CONGRUENT NUMBERS FRANZ LEMMERMEYER Abstract. In this article we study the Tate-Shafarevich groups corresponding to 2-isogenies of the curve Ek : y 2 = x(x2 − k2 ) and construct infinitely many exa Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:03:50 Analytic number theory Symbol Quadratic reciprocity Elliptic curve Spectral theory of ordinary differential equations Μ operator Abstract algebra Mathematics Number theory
26	Number Theory: A Contemporary Introduction Pete L. Clark Contents Chapter 1. The Fundamental Theorem and Some Applications 1. Foundations Add to Reading List Source URL: math.uga.edu Language: English - Date: 2014-09-04 01:56:58 Algebraic number theory Ring theory Integer sequences Modular arithmetic Prime number Multiplicative function Quadratic reciprocity Coprime Integral domain Abstract algebra Mathematics Number theory
27	Contemplations of an octogenarian mathematician∗ Peter Roquette[removed] ∗ Add to Reading List Source URL: www.rzuser.uni-heidelberg.de Language: English - Date: 2014-09-24 01:36:53 Algebraic number theory Modular arithmetic Quadratic residue Mental calculators Number theorists Emmy Noether Quadratic reciprocity Leonhard Euler Topology Mathematics Abstract algebra Number theory
28	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
29	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
30	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

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