Tag: rational-points

96 Estimating the size of solutions of a diophantine equation 2016-01-05T16:55:40.637

29 Patterns among integer-distance points 2013-07-28T00:35:27.390

23 Does every convex polyhedron have a combinatorially isomorphic counterpart whose faces all have rational areas? 2013-05-04T21:05:52.657

22 Why is there a $\sqrt{5}$ in Hurwitz's Theorem? 2015-07-07T19:10:41.480

19 Does $(x^2 - 1)(y^2 - 1) = c z^4$ have a rational point, with z non-zero, for any given rational c? 2012-05-19T08:14:41.457

19 Rational points on the "quintic circle" $x^5 + y^5 = 7$ 2015-11-22T07:43:21.043

18 Integer-distance sets 2013-07-17T00:18:42.993

16 Rational points on a sphere in $\mathbb{R}^d$ 2013-03-22T01:34:24.433

16 Identifying Ramanujan's integer solutions of x^3+y^3+z^3=1 among Elkies' rational solutions 2013-06-28T16:00:12.553

15 Is the perimeter of an ellipse with integer axes irrational? 2013-11-23T02:53:04.860

15 Number of height-limited rational points on a circle 2015-09-28T13:03:56.307

15 Determining the Mordell-Weil group of a universal elliptic curve 2017-10-10T06:59:46.017

14 Totally rational polytopes 2011-08-03T01:29:14.860

14 Rational solutions of the Fermat equation $X^n+Y^n+Z^n=1$ 2015-12-14T18:37:20.517

13 Existence of points on varieties which avoid a given number field. 2012-06-11T19:51:48.333

13 Rational Points on $y^2=x^3-86069^5$ 2012-08-26T21:58:35.453

13 Elliptic curves and connected components 2015-01-23T21:24:45.070

12 Closed vs Rational Points on Schemes 2010-02-02T22:51:59.597

12 Rational points à la Chabauty-Coleman 2011-03-25T23:52:55.560

12 what is the maximum number of rational points of a curve of genus 2 over the rationals 2012-07-27T16:32:14.273

12 Existence of local sections 2014-04-06T02:31:36.743

11 Can a harmonic number be a rational number for non-integer rational argument? 2013-05-07T01:01:27.260

11 Geometrically unirational varieties that are not unirational 2013-06-17T12:46:02.173

11 What evidence is there that $\mathbb{Q}^{ab}$ is ample? 2013-06-23T19:38:12.007

11 What is our current knowledge on the structure of J_0(N)(Q) and J_1(N)(Q) 2014-05-19T13:17:40.027

11 Galois Representations and Rational Points 2017-01-18T06:12:42.297

10 Circles avoiding rational points of height $\le h$ 2014-07-31T23:02:10.470

10 Schoenberg's Rational Polygon Problem 2014-10-12T01:33:31.943

10 rational points of a hyperelliptic curve 2014-12-02T03:28:10.850

10 How much do I need to learn algebraic geometry to understand arithmetics over number fields 2016-04-07T22:01:53.383

10 Possible groups of K-rational points for elliptic curves over arbitrary fields 2017-09-06T09:00:39.760

9 Existence of hyperelliptic curve with specific number of points in a family 2009-11-10T17:29:32.807

9 Rational points on surfaces of general type 2013-03-07T12:40:00.257

9 Rational points on circular spirals 2013-09-08T00:55:29.703

8 Shortest irrational path 2011-07-26T12:13:52.230

8 Smart elliptic curve rational point search given Reg*#Sha 2012-02-04T06:26:27.373

8 Varieties with infinitely many etale covers and rational points 2012-11-03T01:19:50.017

8 Distribution of Mordell–Weil ranks of higher genus curves 2015-06-06T20:51:04.920

8 An elliptic curve for Ramanujan-type cubic identities? 2016-07-04T21:42:50.913

8 Scaling a set of reals to be nearly integers 2017-08-15T11:45:05.773

8 Artin representations appearing in Mordell-Weil groups of elliptic curves 2017-09-07T13:10:42.520

7 Sums of cubes and more 2009-10-13T19:52:05.320

7 Lattice radial-step (ratchet) spirals 2013-10-26T18:46:30.013

7 Endomorphism algebras of abelian surfaces with real multiplication 2015-05-29T11:42:03.320

7 What is the exact statement about uniform boundedness of rational points on curves of genus greater than one? Singular points can be unbounded 2015-11-18T12:08:17.083

7 Does Chabauty-Coleman method give an algorithm for finding rational points? 2016-09-11T15:52:08.523

7 Rational points on varieties over local fields 2017-10-07T08:26:59.843

7 Why study unirational and rational varieties? 2017-11-30T06:05:25.897

6 How can you find small denominators inside triangles? 2009-10-04T20:19:43.440

6 Rational points on smooth compactifications 2012-05-03T00:18:56.200

6 Simple field extension and rational points 2013-03-31T05:58:54.857

6 Pick's Theorem for rational points of bounded height 2013-07-01T11:45:59.817

6 Is the following consequence of the Lang conjecture known? 2014-01-27T15:35:47.673

6 Rational points techniques on curves not using their Jacobian 2014-08-23T23:01:51.980

6 Average height of rational points on a curve 2015-04-25T01:45:21.160

6 Why are some solutions of these diophantine equations off the usual patterns? 2015-12-07T09:22:31.633

6 If $X$ is a genus $g\geq 2$ curve over a number field $K$, then is there a bound on $X_L(L)$ for $L/K$ that depends only on $X$ and $[L:K]$? 2016-10-19T00:46:36.987

6 rational points and a local perturbation of an elliptic curve 2017-11-06T20:45:16.260

6 What is the smallest sphere whose surface includes 100 integer points? 2018-01-30T14:32:52.307

5 Existence of a non-trivial zero (in the rational cyclotomic field) of a form 2011-10-11T06:52:50.227

5 12 descent scripts for pari/gp 2012-09-13T04:05:16.270

5 Solving for special rational triangles 2013-06-25T12:07:53.343

5 Maximum number of general-position points with mutual rational distances? 2014-10-05T00:42:00.940

5 Transcendental distance sets 2015-07-26T14:15:41.687

5 A relative version of Hensel's lemma? 2015-09-14T18:28:08.067

5 Counting square zero forms over finite fields 2015-09-21T09:49:28.080

5 Rational $d$-simplices 2016-04-23T00:42:44.000

4 Rational points on $X_0(15)$ 2013-07-02T16:12:31.333

4 What is the complexity of finding an integral point on an elliptic curve? 2014-09-28T08:11:10.800

4 Find all possible rational values of a parametric quartic such that it is reducible 2015-04-06T20:44:45.353

4 Find all rational solutions of this diophantine-equation? 2015-06-07T14:34:25.970

4 Conics, rational points and probability 2015-12-23T17:26:21.080

4 Rational points on the unit circle 2016-08-02T23:24:23.143

4 Understanding Siegel's Theorem on integral points 2016-12-16T16:34:00.507

4 Action of the Picard Scheme of an Elliptic Fibration 2018-02-06T12:05:36.987

4 Integral complete 4-partite graphs 2018-02-17T21:29:00.193

3 k rational points and base change 2011-05-25T12:28:15.813

3 Brauer-Manin obstruction and Hasse principle 2012-01-03T17:13:40.113

3 How many points are there on an elliptic curve reduced at a bad prime? 2012-05-31T07:15:20.070

3 Rational points and Tesla cards 2012-12-12T01:39:39.580

3 Closed points of field extension of k-scheme under projection 2013-09-02T18:45:54.157

3 Lattice-point-free buffers around circles 2013-10-30T12:15:39.503

3 cohomological obstructions and rational points 2015-01-28T19:53:19.803

3 Existence of lattices whose circles have bounded number of points 2016-07-11T14:48:37.603

2 Rational subspaces 2012-10-03T04:03:59.227

2 Question on x coordinates of Mordell Curves where $y^2=x^3+k$ and $k^2 = 1$ mod $24$ 2013-08-03T10:37:55.767

2 The uniform boundedness of rational torsion for traceless abelian surfaces over a function field 2014-12-23T14:50:38.967

2 Rank of the Jacobian of twists of hyperelliptic curves 2015-08-23T05:45:33.907

2 F-points of product of closed subgroups vs. product of F-points, F a local field, reference? 2015-11-25T23:51:59.747

2 Rational points on towers of curves 2015-12-27T20:05:42.590

2 the least point on a variety over a finite field 2016-03-20T07:59:07.333

2 Counting algebraic points of bounded height 2017-11-11T18:12:30.947

2 Number of rational points of a singular cubic surface over a finite field 2017-11-12T07:07:51.430

1 are p-limits scales dense in the infinite musical scale of all rational frequencies? 2012-07-14T22:40:22.283

1 Tricks to produce examples of hypersurfaces with index greater than $1$ 2013-04-06T18:51:35.120

1 Infinite residue field extensions and algebraic closure of residue fields 2013-09-05T16:28:48.527

1 Existence of a curve with no points over finite separable field extensions 2013-09-11T09:58:39.000

1 Benchmark problems for computing rational points on varieties 2014-01-08T20:23:35.893

1 Coarse moduli spaces and rational points 2014-06-07T21:50:06.877