Tag: number-fields

51 Degree of sum of algebraic numbers 2010-06-02T15:14:06.707

34 Does every ring of integers sit inside a monogenic ring of integers? 2016-05-04T19:09:38.740

33 Simple argument regarding sums of two units in a number field? 2015-10-05T15:52:12.933

29 Which number fields are monogenic? and related questions 2010-04-13T22:01:21.310

26 Are there two non-isomorphic number fields with the same degree, class number and discriminant? 2009-10-30T16:04:22.713

24 Orders in number fields 2013-05-08T15:50:58.317

23 Global fields: What exactly is the analogy between number fields and function fields? 2009-10-20T04:28:40.850

22 Why are polynomials so useful in mathematics? 2014-06-13T01:10:17.903

21 The divisor bound in number fields 2011-06-21T21:23:06.587

20 What is the ring of integers of the Pythagorean field? 2010-07-27T16:07:57.343

20 Are class numbers encoded in the absolute Galois group of ${\mathbb Q}$? 2010-12-20T13:27:49.360

19 How random are unit lattices in number fields? 2010-10-10T22:28:35.793

17 A set of generators for $\bar{\mathbb{Q}}$ 2015-09-14T17:57:03.207

17 Can the Dedekind zeta function distinguish between real and imaginary quadratic number fields? 2016-02-28T15:45:17.693

16 sum of squares in ring of integers 2010-02-07T03:45:26.143

15 What's so special about these $17$th deg equations? 2015-12-18T14:25:35.347

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

14 Solving polynomial equations when you know in which number field the solutions live 2009-10-25T00:03:54.620

14 Families of number fields of prime discriminant 2010-01-04T21:33:34.890

14 Given a number field $K$, when is its Hilbert class field an abelian extension of $\mathbb{Q}$? 2010-02-19T03:48:45.217

14 Which polynomials arise as formulas for a conjugate 2011-01-28T12:23:24.597

14 $Q(\sqrt{2})=Q((\sqrt{2}+1)^n)$ 2011-09-26T09:26:48.737

13 A problem on Algebraic Number Theory, Norm of Ideals 2009-12-18T03:13:07.290

13 Computing (on a computer) higher ramification groups and/or conductors of representations. 2010-03-05T19:34:18.713

12 Records for low-height points on elliptic curves over number fields 2011-10-06T15:22:18.080

11 Irreducible polynomial over number field with roots in every completion? 2009-11-29T00:33:13.943

11 A congruence involving roots of unity 2017-11-01T19:46:49.043

10 Is there an analog of class field theory over an arbitrary infinite field of algebraic numbers? 2010-04-02T14:51:58.130

10 Why the roots of unity are the analogs of constants ? 2010-06-14T13:55:23.933

10 local-global principle for units 2011-05-31T08:35:22.790

10 Can there be a power basis for a totally real field of high degree? 2014-08-08T12:32:35.377

9 Which computer algebra system should I be using to solve large systems of sparse linear equations over a number field? 2009-10-25T20:14:03.840

9 Subfields joining an algebraic element to another 2009-12-08T12:48:04.150

9 Irreducibility of the trinomial over Q 2013-06-19T20:12:00.853

9 Go I Know Not Whither and Fetch I Know Not What 2014-09-16T01:58:45.450

9 class number of prime degree field with prime conductor 2016-09-01T03:54:34.110

9 Upper bounds for regulators of real quadratic fields 2016-10-23T16:14:21.183

8 Extension of valuation 2010-07-05T04:23:17.980

8 If the n-th root of unity exists locally, does it exist globally? 2010-12-22T03:35:05.350

8 The "interplay" between additive and multiplicative structure in a field 2013-03-16T22:14:05.407

8 Quintic polynomial solution by Jacobi Theta function. 2013-06-16T11:04:42.507

8 Euclidean real quadratic fields 2013-10-17T14:09:26.860

8 The Stickelberger's annihilation theorem over an arbitrary number field 2017-08-16T06:07:43.967

7 number fields generated by units of number fields 2010-06-07T19:27:54.203

7 Given $v,w$ primes of $k$, is there $K/k$ so $K_v\cap\Bbb Q^{cycl}=K_w\cap\Bbb Q^{cycl}=K\cap\Bbb Q^{cycl}$? 2010-06-10T02:28:37.283

7 Is it known if the absolute Galois group is "divisible"? 2012-11-28T17:55:55.380

7 Number of ways to write an integer as a product of irreducibles 2013-11-04T18:46:46.937

7 Degree of Kummer extensions of number fields 2014-03-16T13:53:24.150

7 Is realness of number fields exponentially bounded? 2014-03-16T19:18:48.403

7 Continued fraction expansion of an algebraic number and its conjugates 2014-07-16T16:16:44.410

7 The density of minimal polynomials 2017-10-20T13:25:04.607

6 Dirichlet's theorem for number fields 2010-06-23T04:57:31.243

6 What is the set of possible values of the degree of the sum of two algebraic numbers with fixed degrees? 2010-07-01T07:18:41.130

6 Why is every quadratic subfield of a Galois extension of the rationals with the quaternions as Galois group real? 2010-09-16T09:08:13.013

6 Simultaneous Powers Far From 1 2013-06-25T17:49:04.953

6 Isomorphism problem for two radical extensions 2014-11-26T18:45:58.963

6 Do all algebraic number fields arise from Eisenstein polynomials? 2015-02-20T09:03:05.223

6 Number of representations as sums of squares in rings of integers of number fields 2015-08-04T23:01:29.963

6 Unramified extensions of quadratic fields 2015-12-21T03:22:16.737

5 How many primes stay inert in a finite (non-cyclic) extension of number fields? 2010-01-20T02:20:02.233

5 Transformations of integer polynomials under combinations of their roots 2010-04-15T07:40:24.180

5 Elliptic curve with no points in a number field 2011-12-23T10:22:54.963

5 Are the Szpiro ratios of 37b1 over certain number fields {33,39,42,48,51,66}? 2014-09-20T06:03:23.077

5 Primitive element for a number field, and ramification 2016-05-22T03:04:02.273

5 free subgroups of $SL_2(\mathbb{Z[i]})$ 2016-09-12T09:28:47.053

4 Is there a section disjoint from 0, 1 and infinity on the projective line 2011-09-23T13:44:00.150

4 Subject to some conditions, is it possible to conclude a subfield of an abelian extension generated by a unit is a cyclic extension 2012-04-09T01:49:46.820

4 On class numbers $h(-d)$ and the diophantine equation $x^2+dy^2 = 2^{2+h(-d)}$ 2013-11-11T22:26:07.633

4 Number field of degree 5 2014-02-07T12:33:16.707

4 unit group of biquadratic fields 2014-05-08T07:35:28.140

4 p-adic expansion for elements in algebraic closure of p-adic numbers 2016-12-01T23:26:50.620

4 Annihilator of a closed subgroup of adeles 2017-05-15T13:47:33.997

4 Are there primitive quartic CM fields whose norms of units give all totally positive units of the real quadratic subfield? 2017-06-28T13:34:18.650

4 Unramified non-abelian extension and Galois cohomology 2018-02-25T16:29:03.557

3 Why isn't there a structure with two primes? 2010-04-01T15:53:12.070

3 Distribution of associate primes modulo q in number fields 2010-06-23T16:51:04.780

3 Irreducibility of trinomials 2013-08-08T18:42:47.683

3 Irreducibility of trinomials over number fields 2013-08-20T19:40:46.007

3 Definability of orderings on a formally real number field 2013-12-16T13:47:06.207

3 A question about "small" sets of algebraic numbers 2015-06-19T00:45:06.653

3 Interpretation or application of this analog of minimal polynomial 2018-01-18T22:02:25.410

2 Continuation up to zero of a Dirichlet series with bounded coefficients 2010-01-09T20:23:41.170

2 Unit in a number field with same absolute value at a real and a complex place 2010-03-10T13:25:15.183

2 A subring question (revised) 2011-01-19T04:06:03.223

2 Which numbers appear as discriminants of cubics? 2011-02-18T14:18:05.233

2 bounds for the covering radius (or diameter of the Voronoi cell) of a lattice coming from a number field 2011-11-16T14:15:04.747

2 Is there a Dirichlet Unitary Unit Theorem? 2012-05-18T15:50:42.820

2 Comparing ideal class numbers of different orders 2012-11-15T14:18:41.110

2 Useful notion of unramified Galois representation 2012-12-19T22:01:09.880

2 ramification of discrete valuation field 2013-04-24T12:39:02.873

2 Full $n$-torsion of elliptic curves and the cyclotomic field of order $n$ 2013-05-24T08:27:05.597

2 Lower Degree Elements in an Algebraic Number Field 2013-06-19T15:21:29.373

2 Lowest degree polynomial with integer coefficients yielding $1/\sqrt{2^n}$ 2014-10-02T20:59:08.230

2 "frequency" of fields for which the p-adic regulator vanishes (mod p) 2015-04-04T20:33:30.297

2 Normal basis in cyclotomic number fields 2015-04-06T15:29:11.257

2 Automorphism group of $\mathbf{C}$ over $\overline{\mathbf{Q}}$ 2016-04-11T21:50:41.413

2 Can there be a numerical system in which logarithms can be expressed in terms of exponentials in closed form? 2016-05-03T09:59:29.143

2 relation between class number of an algebraic number field and its Galois closure 2016-09-17T12:57:30.850

2 Valuation topology vs modified valuation topology 2016-12-03T00:34:58.323