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Geometry of numbers
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#	Item
131	THREE NEW FACTORS OF FERMAT NUMBERS R. P. BRENT, R. E. CRANDALL, K. DILCHER, AND C. VAN HALEWYN Abstract We report the discovery of a new factor for each of the Fermat numbers F13 , F15 , F16 . These new factors have 27, Add to Reading List Source URL: gan.anu.edu.au Language: English - Date: 2003-11-05 11:07:22 Integer sequences Integer factorization algorithms Euclidean plane geometry Fermat number Number theory Pierre de Fermat Lenstra elliptic curve factorization Integer factorization Richard P. Brent Mathematics Abstract algebra Group theory
132	Mathematical Olympiad in Poland Second Round, February 25–26, 2000 First Day 1. Prove or disprove the following statement: Each positive rational number can be written in the form a 2 + b3 Add to Reading List Source URL: www.mimuw.edu.pl Language: English - Date: 2000-11-24 10:18:26 Triangle Incircle and excircles of a triangle Polynomial Angle Algebraic numbers Pythagorean theorem Geometry Triangle geometry Triangles
133	Irrationality of The Square Root of Two -- A Geometric Proof Author(s): Tom M. Apostol Source: The American Mathematical Monthly, Vol. 107, No. 9 (Nov., 2000), pp[removed]Published by: Mathematical Association of Americ Add to Reading List Source URL: www-fourier.ujf-grenoble.fr Language: English - Date: 2010-10-07 04:23:25 Euclidean geometry Triangle geometry Euclidean plane geometry Irrational numbers Mathematical constants Square root of 2 Pythagorean theorem Triangle Mathematical proof Geometry Mathematics Triangles
134	The Bulletin of Symbolic Logic Volume 18, Number 1, March 2012 THE ABSOLUTE ARITHMETIC CONTINUUM AND THE UNIFICATION OF ALL NUMBERS GREAT AND SMALL Add to Reading List Source URL: www.ohio.edu Language: English - Date: 2012-01-31 12:26:37 Real algebraic geometry Mathematical logic Field theory Real closed field Philip Ehrlich Infinitesimal Surreal number Real number Archimedean property Mathematics Abstract algebra Infinity
135	Margulis Numbers of Hyperbolic 3-Manifolds Peter Shalen August 21, 2010 Margulis numbers Add to Reading List Source URL: www2.ims.nus.edu.sg Language: English - Date: 2010-08-21 11:37:14 Space Hyperbolic geometry Geometric topology Riemannian manifolds Hyperbolic manifold Haken manifold Margulis lemma Hyperbolic 3-manifold Differentiable manifold Topology Geometry 3-manifolds
136	A SHARPER ESTIMATE ON THE BETTI NUMBERS OF SETS DEFINED BY QUADRATIC INEQUALITIES SAUGATA BASU AND MICHAEL KETTNER Abstract. In this paper we consider the problem of bounding the Betti numbers, bi (S), of a semi-algebrai Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:31:16 Quadratic forms Algebraic topology Betti number Topological graph theory Algebraic geometry Real algebraic geometry Algebraic variety Weil conjectures Algebra Mathematics Abstract algebra
137	BOUNDING THE EQUIVARIANT BETTI NUMBERS AND COMPUTING ´ CHARACTERISTIC OF THE GENERALIZED EULER-POINCARE SYMMETRIC SEMI-ALGEBRAIC SETS SAUGATA BASU AND CORDIAN RIENER Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2014-01-17 21:15:39 Algebraic topology Algebraic geometry Field theory Polynomials Betti number Homogeneous polynomial Algebraic variety Symmetric polynomial Real algebraic geometry Abstract algebra Algebra Mathematics
138	POLYNOMIAL HIERARCHY, BETTI NUMBERS AND A REAL ANALOGUE OF TODA’S THEOREM SAUGATA BASU AND THIERRY ZELL Abstract. Toda [36] proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the class P# Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:44:12 Field theory Real algebraic geometry Algebraic geometry Real closed field Betti number Polynomial Algebraic variety Field Semialgebraic set Abstract algebra Mathematics Algebra
139	ON THE BETTI NUMBERS OF SIGN CONDITIONS SAUGATA BASU, RICHARD POLLACK, AND MARIE-FRANC ¸ OISE ROY Abstract. Let R be a real closed field and let Q and P be finite subsets of R[XV1 , . . . , Xk ] such that the set P has Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:45 Orbifold Algebraic geometry Algebraic variety Μ operator
140	COMPUTING THE BETTI NUMBERS OF SEMI-ALGEBRAIC SETS DEFINED BY PARTLY QUADRATIC SYSTEMS OF POLYNOMIALS SAUGATA BASU, DMITRII V. PASECHNIK, AND MARIE-FRANC ¸ OISE ROY Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:26 Algebraic geometry Betti number Polynomial Semialgebraic set Ordinal number Probability theory Transcendental number Probability space Mathematics Abstract algebra Real algebraic geometry

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