Vela Mathematics Program: problems

Narrowed tonot formalized ×analysis ×Clear all

Problem ledger

42 problemsGraph view

declared falsifiable · $250erdos:114

Erdős problem 114

polynomialsanalysisN/A

declared provederdos:116

Erdős problem 116

polynomialsanalysisN/A

declared provederdos:225

Erdős problem 225

analysisN/A

declared disprovederdos:227

Erdős problem 227

analysisN/A

declared disprovederdos:230

Erdős problem 230

analysispolynomialsN/A

declared openerdos:256

Erdős problem 256

analysisN/A

declared provederdos:395

Erdős problem 395

analysisN/A

declared provederdos:485

Erdős problem 485

analysispolynomialspossible2 sources

declared disprovederdos:511

Erdős problem 511

analysisN/A

declared openerdos:514

For a transcendental entire function, how fast can

|f(z)|

be forced to grow along a path to infinity, and how short can such a path be in terms of the maximum modulus

M(r, f)

analysisN/A4 sources

declared provederdos:515

Erdős problem 515

analysisN/A

declared provederdos:523

Erdős problem 523

analysisprobabilitypolynomialsN/A

declared openerdos:524

Erdős problem 524

analysisprobabilitypolynomialsN/A3 sources

declared provederdos:525

Erdős problem 525

analysisprobabilitypolynomialspossible

declared provederdos:527

Erdős problem 527

analysisprobabilityN/A

declared open · $250erdos:671

For triangular arrays of nodes

a_i^n\in[-1,1]

let

\mathcal{L}^nf

be the Lagrange interpolation polynomials of a continuous

f

, with fundamental polynomials

p_i^n

. Is there a choice of nodes such that for every continuous

f

there is some

x

where

\limsup_n \sum_i\lvert p_{i}^n(x)\rvert=\infty

and yet

\mathcal{L}^nf(x) \to f(x)

? Is there a choice with

\limsup_n \sum_i\lvert p_{i}^n(x)\rvert=\infty

for every

x

, yet for every continuous

f

some

x

has

\mathcal{L}^nf(x)\to f(x)

? Both questions are claimed resolved in the affirmative.

analysisN/A3 sources

declared provederdos:908

Erdős problem 908

analysisN/A

declared provederdos:909

Erdős problem 909

analysistopologyN/A

declared disprovederdos:994

Erdős problem 994

analysisdiscrepancyN/A

declared openerdos:995

Erdős problem 995

analysisdiscrepancyN/A2 sources

declared provederdos:998

Erdős problem 998

analysisdiophantine approximationN/A

declared openerdos:1039

For

f(z) = \prod_{i=1}^n (z - z_i)

with all

|z_i| \le 1

, let

\rho(f)

be the radius of the largest disc contained in

\{z : |f(z)| < 1\}

. Is

\rho(f) \gg 1/n

? The worst case is now known to be

\Theta(1/n)

, with the explicit bound

\rho(f) \ge (\log 2)/n

analysisN/A3 sources

declared openerdos:1040

For a closed infinite set

F \subseteq \mathbb{C}

, let

\mu(F)

be the infimum of

|\{z : |f(z)| < 1\}|

over monic polynomials with zeros in

F

. Is

\mu(F)

determined only by the transfinite diameter of

F

analysisN/A3 sources

declared provederdos:1042

Erdős problem 1042

analysisN/A

declared openerdos:1045

Erdős problem 1045

analysisN/A

declared disprovederdos:1046

Erdős problem 1046

analysisN/A

declared provederdos:1114

Erdős problem 1114

analysispolynomialsN/A

declared solvederdos:1115

Erdős problem 1115

analysisN/A

declared solvederdos:1116

Erdős problem 1116

analysisN/A

declared openerdos:1117

Erdős problem 1117

analysisN/A

declared solvederdos:1118

Erdős problem 1118

analysisN/A

declared openerdos:1120

Erdős problem 1120

analysisN/A

declared provederdos:1129

Erdős problem 1129

analysispolynomialsN/A2 sources

declared provederdos:1130

Erdős problem 1130

analysispolynomialsN/A2 sources

declared openerdos:1131

Erdős problem 1131

analysispolynomialsN/A2 sources

declared openerdos:1132

Erdős problem 1132

analysispolynomialsN/A2 sources

declared openerdos:1151

Let

\mathcal{L}^nf

be the Lagrange interpolation polynomials of a continuous

f

on the Chebyshev nodes. Prove that, for any closed

A\subseteq [-1,1]

, there exists a continuous function

f

such that

A

is the set of limit points of

\mathcal{L}^nf(x)

analysispolynomialsN/A3 sources

declared openerdos:1152

Erdős problem 1152

analysispolynomialsN/A

declared provederdos:1153

Erdős problem 1153

analysispolynomialsN/A3 sources

declared not disprovableerdos:1154

Erdős problem 1154

analysisN/A

declared disproved (Lean)erdos:1197

Erdős problem 1197

analysisN/A5 sources

declared disprovederdos:1215

Erdős problem 1215

analysisN/A

Problems · Vela Mathematics Program

Problem ledger

Search problems.science