Abstract analytic number theory

Results: 558



#Item
161Analytic number theory / Symbol / Quadratic reciprocity / Elliptic curve / Spectral theory of ordinary differential equations / Μ operator / Abstract algebra / Mathematics / Number theory

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
162Analytic 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

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
163Conic 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

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
164Group theory / Analytic number theory / Deduction / Differential geometry / Modular forms / Elliptic curve / Entailment / Covering space / Differential geometry of curves / Abstract algebra / Mathematics / Topology

A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields Seigo Arita∗ Kazuto Matsuo∗†

Add to Reading List

Source URL: eprint.iacr.org

Language: English - Date: 2004-09-16 01:27:33
165Algebraic curves / Riemann surfaces / Analytic number theory / Abelian varieties / Algebraic structures / Modular form / Divisor / Schottky problem / Abelian integral / Abstract algebra / Algebraic geometry / Mathematical analysis

BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 6, Number 2, March 1982 PROBLEMS ON ABELIAN FUNCTIONS AT THE TIME OF POINCARÉ AND SOME AT PRESENT1

Add to Reading List

Source URL: www.ams.org

Language: English - Date: 2010-01-14 12:42:58
166Algebraic 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

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
167Analytic number theory / Elliptic curve / Group theory / Torsion subgroup / Torsion tensor / Torsion / Analytic torsion / Lenstra elliptic curve factorization / Abstract algebra / Differential geometry / Curvature

HIGH RANK ELLIPTIC CURVES WITH PRESCRIBED TORSION GROUP OVER QUADRATIC FIELDS JULIÁN AGUIRRE, ANDREJ DUJELLA, MIRELA JUKI‚ BOKUN, AND JUAN CARLOS PERAL There are 26 possibilities for the torsion group of elliptic curve

Add to Reading List

Source URL: bib.irb.hr

Language: English - Date: 2014-07-23 10:58:32
168Mathematics / Triangle geometry / Proofs involving the Moore–Penrose pseudoinverse / Pythagorean theorem / Analytic number theory / Elliptic curve / Group theory

On the torsion group of elliptic curves induced by D(4)-triples Andrej Dujella and Miljen Miki´c Abstract A D(4)-m-tuple is a set of m integers such that the product of

Add to Reading List

Source URL: bib.irb.hr

Language: English - Date: 2013-10-08 15:27:22
169Number theory / Analytic number theory / Elliptic curves / Group theory / Birch and Swinnerton-Dyer conjecture / Congruent number / Exponentiation / Angle / Curve / Mathematics / Abstract algebra / Geometry

ON THE HIGH RANK π/3 AND 2π/3-CONGRUENT NUMBER ELLIPTIC CURVES A. S. JANFADA, S. SALAMI, A. DUJELLA, AND J. C. PERAL Abstract. Consider the elliptic curves given by

Add to Reading List

Source URL: bib.irb.hr

Language: English - Date: 2012-10-20 07:52:34
170Elliptic curves / Abelian varieties / Finite fields / Diophantine geometry / Analytic number theory / Mordell–Weil theorem / Elliptic function / Victor S. Miller / Birch and Swinnerton-Dyer conjecture / Abstract algebra / Mathematics / Algebraic geometry

Elliptic Curve Cryptography: Invention and Impact: The invasion of the Number Theorists Victor S. Miller IDA Center for Communications Research Princeton, NJ[removed]USA

Add to Reading List

Source URL: www.iacr.org

Language: English - Date: 2007-06-12 08:54:49
UPDATE