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421	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
422	APn80 Northern Spruce Bog fact sheet Add to Reading List Source URL: files.dnr.state.mn.us Language: English - Date: 2009-10-01 15:33:14 Landforms Mosses Pedology Bog Peat Sphagnum Poor fen Larix laricina Picea mariana Flora Physical geography Wetlands
423	THE EUCLIDEAN ALGORITHM IN ALGEBRAIC NUMBER FIELDS FRANZ LEMMERMEYER Abstract. This article, which is an update of a version published 1995 in Expo. Math., intends to survey what is known about Euclidean number fields; Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2004-02-13 18:30:23 Ring theory Commutative algebra Euclidean algorithm Linear algebra Greatest common divisor Norm Principal ideal domain Euclidean domain Abstract algebra Algebra Mathematics
424	Postscript Helmut Koch, Franz Lemmermeyer During the 30 years since the publication of the German original of this book, the theory of pro-p extensions was flourishing: new results were proved, new insights gained, and Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 14:17:16 Algebraic number theory Field theory Class field theory Group theory Golod–Shafarevich theorem Hilbert class field Algebraic number field Ramification group Field arithmetic Abstract algebra Algebra Galois theory
425	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
426	CONGRUENT NUMBERS, ELLIPTIC CURVES, AND MODULAR FORMS GUY HENNIART 1. Invitation to the voyage An integer n ≥ 1 is called congruent if it is the area of a right triangle Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:03:29 Analytic number theory Number theory Group theory Elliptic curve Modular forms Finite fields Birch and Swinnerton-Dyer conjecture Algebraic number field Complex multiplication Abstract algebra Mathematics Mathematical analysis
427	APn81 ACID PEATLAND SYSTEM Northern Floristic Region Northern Poor Conifer Swamp Add to Reading List Source URL: files.dnr.state.mn.us Language: English - Date: 2009-09-29 13:26:12 Wetlands Ecoregions of Canada Nearctic Larix laricina Eriophorum Aspen parkland Poor fen Bog Tussock Physical geography Geography of Canada Biogeography
428	CONICS - A POOR MAN’S ELLIPTIC CURVES FRANZ LEMMERMEYER Contents Introduction 1. The Group Law on Pell Conics and Elliptic Curves Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-11-17 18:14:51 Conic sections Number theory Algebraic curves Analytic number theory Curves Elliptic curve Birch and Swinnerton-Dyer conjecture Degenerate conic Modular form Geometry Algebraic geometry Abstract algebra
429	GALOIS GROUPS ATTACHED TO POINTS OF FINITE ORDER ON ELLIPTIC CURVES ` SERRE) OVER NUMBER FIELDS (D’APRES ´ JACQUES VELU Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:04:08 Elliptic curve Subgroup Symmetric group Projective linear group Fundamental theorem of Galois theory Abstract algebra Algebra Group theory
430	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

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