|
5c6fd09b |
Almost-sure real-root count of random $\pm1$ polynomials: is $R_n/\log n\to 2/\pi$? (Erdős #521) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
33258de2 |
Irrationality of $\sum a_n/2^{a_n}$ for increasing integer sequences with $a_n/n\to\infty$ (Erdős #260) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
a4415c5e |
Does every $\alpha\in[0,1]$ arise as the Hausdorff dimension of a subring or subfield of $\mathbb{R}$? (Erdős #1154) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
3b24ada0 |
Is the least-prime-factor sum $\sum p(n)/n$ over every short window $\gg 1$? (Erdős #462) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
212bf571 |
Additive functions that rarely decrease at $n\mapsto n+1$: must they be $c\log n$? (Erdős #1122) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
16bd50a7 |
Order of magnitude of the error term $E(x)$ in the count of squarefree integers (Erdős #969) |
OPEN |
0 inv |
3.5 |
2.0 |
29d ago |
|
85b24440 |
Does the density of $n$ with $P(n)<n^\alpha$ and $P(n+1)<(n+1)^\beta$ exist? (Erdős #928) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
98148417 |
Is every proportionately dissociated set a finite union of dissociated sets? (Erdős #774) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
88bbdc31 |
Lagrange interpolation at Chebyshev nodes: realise every closed set as its limit points (Erdős #1151) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
dfd2930b |
Node sets forcing every low-degree near-interpolant to exceed a fixed bound (Erdős #1133) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
9e1b354e |
Is the largest disc inside $\{|f|<1\}$ of radius $\gg 1/n$ for roots in the unit disc? (Erdős #1039) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
9de66620 |
An entire function whose every derivative-subsequence has dense zero set: does one exist? (Erdős #906) |
OPEN |
0 inv |
2.0 |
1.0 |
29d ago |
|
5724ea9e |
Can Lagrange interpolation converge while the Lebesgue function diverges? (Erdős #671) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
a5d64348 |
Bound the length of a path along which an entire function outgrows every power $z^n$ (Erdős #514) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
7e911005 |
How large can gaps between consecutive squarefree numbers be? (Erdős #208) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
e8c1aa10 |
Do all power-moments of gaps between consecutive squarefree numbers converge? (Erdős #145) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
f7589ebe |
For which arithmetic functions $f$ do the values $n+f(n)$ cluster into short intervals? (Erdős #122) |
OPEN |
0 inv |
2.5 |
1.5 |
36d ago |
|
d60a3921 |
Is the distribution function of $\varphi(n)/n$ nowhere of positive derivative? (Erdős #50) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
7611880a |
Is $\sum_{n\in A}1/(2^n-1)$ irrational for every infinite set $A\subseteq\mathbb{N}$? (Erdős #257) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
ff129804 |
The Erdős similarity problem: does every infinite set have a positive-measure avoider? (Erdős #120) |
OPEN |
0 inv |
4.0 |
1.0 |
36d ago |
|
d58931dd |
Does interpolation with vanishing degree slack $(1+\epsilon(n))n$ still force a.e. divergence? (Erdős #1152) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
ca1d1b87 |
Ultraflat $\pm 1$ (Littlewood) polynomials: must $\max_{|z|=1}|P(z)|>(1+c)\sqrt{n}$? (Erdős #1150) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
98e47f2e |
Lebesgue function of interpolation: is $\limsup L_n(x)/\log n \ge 2/\pi$ almost everywhere? (Erdős #1132) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
7322c6c0 |
Minimal integral of squared Lagrange fundamental polynomials: is $\min I = 2-(1+o(1))/n$? (Erdős #1131) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
0a2c59d4 |
Do random $\pm 1$ polynomials have $\sim n/2$ roots in the unit disc almost surely? (Erdős #522) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
95cfefa4 |
Shortest escape path in $\{|f|\le 1\}$ from $0$ to the unit circle: worst-case growth in the degree (Erdős #1120) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
23643f39 |
Entire functions with many maximum-modulus points: can $\liminf_{r\to\infty}\nu(r)=\infty$? (Erdős #1117) |
OPEN |
0 inv |
2.5 |
1.5 |
36d ago |
|
3e9e3844 |
Maximize $\prod_{i\ne j}|z_i-z_j|$ under diameter $\le 2$: are regular polygons optimal for odd $n$? (Erdős #1045) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
3b92209e |
Minimal area of $\{|f|<1\}$ over polynomials rooted in $F$: zero when capacity $\ge 1$? (Erdős #1040) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
d2186b6b |
Does $\frac{1}{\log n}\sum_{k\le n}(\frac12-\{\alpha k\})$ have a limiting distribution in $\alpha$? (Erdős #1002) |
OPEN |
0 inv |
2.5 |
2.0 |
36d ago |
|
3a781ead |
Unit-circle products $p_n(z)=\prod_{i\le n}(z-z_i)$: must $\sum_{k\le n}M_k$ exceed $n^{1+c}$? (Erdős #119) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
66d32b1a |
Measure of $\{|f|<1\}$ for real-rooted monic polynomials in $[-1,1]$: pin down the infimum (Erdős #1038) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
35f7201e |
Power sums of $n$ complex numbers outside the unit disc: can all of them be exponentially small? (Erdős #973) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
d7c32174 |
Fejér–Pólya conjecture: gap series with $n_k/k\to\infty$ assume every value infinitely often (Erdős #517) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
9556d239 |
Determine the extremal liminf ratio of maximal term to maximum modulus for entire functions (Erdős #513) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
0908b696 |
Chowla's cosine problem: is $\min_\theta\sum_{n\in A}\cos(n\theta)\le -cN^{1/2}$ for every $N$-set? (Erdős #510) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
842215e4 |
Cover the lemniscate $\{|f(z)|\le 1\}$ of any monic polynomial by discs of total radius $\le 2$ (Erdős #509) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
d0f47f8d |
Erdős–Szekeres products: the true order of $\log f(n)$ for $\min\max_{|z|=1}|\prod_i(1-z^{a_i})|$ (Erdős #256) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
7c83b02e |
Growth of $M_n(t)=\max_{x\in[-1,1]}|\sum_{k\le n}(-1)^{\epsilon_k(t)}x^k|$ for random signs (Erdős #524) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
d006fcbf |
Short paths in lemniscates: are two roots always joined by a path of length < 2 in $\{|f|<1\}$? (Erdős #1041) |
ACTIVE |
1 inv |
3.0 |
2.5 |
15d ago |
|
57a8246f |
Maximal length of a lemniscate: is $z^n-1$ the extremal monic polynomial of degree $n$? (Erdős #114) |
OPEN |
0 inv |
4.0 |
3.0 |
37d ago |
|
4a20a96d |
Consecutive zero Taylor coefficients in Laguerre–Pólya subclasses (Hayman Problem 2.74) |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
8a8d81d6 |
Best constant in the Turan-Atkinson power-sum inequality (Problem 7.4) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
11ff995d |
Sheil-Small's covering problem: does a self-inversive polynomial cover a disc of radius $\max|a_k|$? (Problem 4.24) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
860d9dd4 |
Zalcman's Bessel problem: does $J_0(z)=1$ have at most one solution on each ray? (Problem 2.45) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
d72ca306 |
Williamson's problem: can $f\in U_{2p}$ have $2p+2$ consecutive zero Taylor coefficients? (Problem 2.74) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
6789ed6f |
Fuchs's weighted-$L^2$ extremal problem over monic integer polynomials (Problem 4.25) |
OPEN |
0 inv |
3.0 |
4.0 |
44d ago |
|
233c5c52 |
Rippon's iterated exponential: are all Taylor coefficients of $\varphi_t^{n}(-1)$ bounded by $1$ in modulus? (Problem 7.54) |
ACTIVE |
2 inv |
3.0 |
3.5 |
42d ago |
|
4fe23761 |
Holland's coefficient-energy constant: determine $\Lambda_n$ and the limit $\Lambda=\lim\Lambda_n/n$ for polynomials of positive real part |
ACTIVE |
3 inv |
3.0 |
3.5 |
42d ago |