User Vesselin Dimitrov

71 votes

34 answers

12k views

Trichotomies in mathematics

asked Feb 2, 2013 at 20:25

63 votes

3 answers

5k views

Are there infinitely many integer-valued polynomials dominated by $1.9^n$ on all of $\mathbb{N}$?

asked Aug 11, 2013 at 8:47

18 votes

2 answers

2k views

If there is a dense geodesic, are almost all geodesics equidistributed? Dense?

asked Jul 20, 2014 at 19:38

18 votes

1 answer

1k views

How many integers divide a number that involves just three non-zero digits?

asked Aug 9, 2014 at 8:27

17 votes

1 answer

704 views

Is there a bounded sequence of points in the plane with pairwise distances at least $1/\sqrt{|i-j|}$?

asked Nov 18, 2014 at 1:58

15 votes

1 answer

901 views

Does Littlewood's bound on $\zeta(1+it)$ extend to all the partial sums?

asked Jun 23, 2016 at 22:48

14 votes

0 answers

645 views

Can there be arbitrarily many cubic fields unramified outside $\{p,\infty\}$?

asked Feb 2, 2015 at 20:31

14 votes

3 answers

938 views

Asymptotics for algebraic numbers of height less than one

asked Jul 27, 2014 at 20:37

14 votes

2 answers

685 views

Occurrences of D. H. Lehmer's 10-th degree polynomial

asked Sep 4, 2013 at 16:22

13 votes

0 answers

584 views

Should the number of small solutions in Roth's theorem be bounded uniformly, assuming the target is an algebraic integer?

asked Jul 3, 2013 at 11:33

13 votes

0 answers

311 views

Diophantine approximation in the Julia set

asked Mar 7, 2016 at 16:59

13 votes

0 answers

316 views

$p$-Adic or arithmetic variants of Khovanskii's "low complexity $\Rightarrow$ tame topology" theory

asked Aug 12, 2015 at 20:50

13 votes

1 answer

528 views

Are the logarithms of the integer polynomials discrete in $L^1$ of the unit circle?

asked Jun 22, 2019 at 9:26

12 votes

0 answers

657 views

Rational iterations on $\mathbb{P}^1$ defined over $\mathbb{Q}$ and possessing a totally $2$-adic point of a high finite order

asked Sep 25, 2013 at 20:30

12 votes

0 answers

433 views

Average ranks of abelian surfaces

asked Feb 5, 2013 at 23:38

12 votes

1 answer

594 views

The torsion point count in higher dimension

asked Feb 8, 2013 at 14:33

11 votes

2 answers

1k views

Can there be a power basis for a totally real field of high degree?

asked Aug 8, 2014 at 12:32

11 votes

1 answer

485 views

The Mordell and Bogomolov problems in linear groups

asked Aug 15, 2014 at 13:24

11 votes

1 answer

883 views

Higher Fano varieties and Tsen's theorem

asked May 1, 2015 at 23:08

11 votes

0 answers

381 views

What are the possible bad reductions for an abelian variety of dimension $g$ and a maximal endomorphism ring?

asked Jul 2, 2018 at 19:13

10 votes

2 answers

371 views

Refined equidistribution for the periodic trajectories of Anosov flows?

asked Oct 12, 2016 at 20:53

10 votes

1 answer

1k views

The supremum value of $\int f(t) \log{\frac{1}{|t|}} \, dt$ for normalized Fourier pairs non-negative outside of $[-1,1]$

asked Nov 8, 2017 at 23:13

10 votes

1 answer

810 views

An extremal problem related either to an uncertainty principle on the circle, or else to the prime number theorem

asked Dec 8, 2017 at 5:05

10 votes

0 answers

706 views

Paths in $\mathrm{Spec} \, \mathbb{Z}$ and Kim's proof of Siegel's theorem for $\mathbb{P}^1 \setminus \{0,1,\infty\}$

asked Feb 3, 2015 at 18:03

10 votes

2 answers

719 views

The height of an orbit under rational self-maps

asked Jan 30, 2013 at 13:32

10 votes

1 answer

595 views

Are the polynomials in $\{1/t\}$ dense in $L^2(0,1)$?

asked Apr 23, 2019 at 22:10

9 votes

1 answer

499 views

Subspaces of $L^2(0,1)$ dense on every truncation $L^2(c,1)$

asked Apr 24, 2019 at 3:43

9 votes

0 answers

324 views

Discriminants of Gleason's period-$n$ polynomials for the Mandelbrot set

asked Jun 4, 2020 at 22:51

9 votes

1 answer

331 views

What is the set of possible densities of pointless members in a family of rational curves over $\mathbb{Q}$?

asked Sep 28, 2013 at 16:18

9 votes

1 answer

858 views

A question about Mirzakhani et. al.'s algebraicity theorem

asked Mar 17, 2015 at 4:53

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75 Questions

Trichotomies in mathematics

Are there infinitely many integer-valued polynomials dominated by $1.9^n$ on all of $\mathbb{N}$?

If there is a dense geodesic, are almost all geodesics equidistributed? Dense?

How many integers divide a number that involves just three non-zero digits?

Is there a bounded sequence of points in the plane with pairwise distances at least $1/\sqrt{|i-j|}$?

Does Littlewood's bound on $\zeta(1+it)$ extend to all the partial sums?

Can there be arbitrarily many cubic fields unramified outside $\{p,\infty\}$?

Asymptotics for algebraic numbers of height less than one

Occurrences of D. H. Lehmer's 10-th degree polynomial

Should the number of small solutions in Roth's theorem be bounded uniformly, assuming the target is an algebraic integer?

Diophantine approximation in the Julia set

$p$-Adic or arithmetic variants of Khovanskii's "low complexity $\Rightarrow$ tame topology" theory

Are the logarithms of the integer polynomials discrete in $L^1$ of the unit circle?

Rational iterations on $\mathbb{P}^1$ defined over $\mathbb{Q}$ and possessing a totally $2$-adic point of a high finite order

Average ranks of abelian surfaces

The torsion point count in higher dimension

Can there be a power basis for a totally real field of high degree?

The Mordell and Bogomolov problems in linear groups

Higher Fano varieties and Tsen's theorem

What are the possible bad reductions for an abelian variety of dimension $g$ and a maximal endomorphism ring?

Refined equidistribution for the periodic trajectories of Anosov flows?

The supremum value of $\int f(t) \log{\frac{1}{|t|}} \, dt$ for normalized Fourier pairs non-negative outside of $[-1,1]$

An extremal problem related either to an uncertainty principle on the circle, or else to the prime number theorem

Paths in $\mathrm{Spec} \, \mathbb{Z}$ and Kim's proof of Siegel's theorem for $\mathbb{P}^1 \setminus \{0,1,\infty\}$

The height of an orbit under rational self-maps

Are the polynomials in $\{1/t\}$ dense in $L^2(0,1)$?

Subspaces of $L^2(0,1)$ dense on every truncation $L^2(c,1)$

Discriminants of Gleason's period-$n$ polynomials for the Mandelbrot set

What is the set of possible densities of pointless members in a family of rational curves over $\mathbb{Q}$?

A question about Mirzakhani et. al.'s algebraicity theorem