k0 Table

Here is a table of k0 values for (pi_r*ϖ+delta_r*δ < 1) in different pi_r and delta_r settings, generated by a simple nonlinear optimizer.

Each link refers to a maple script ( based on the script in blog by Terence Tao) for a feasible k0. For each k0, the current narrowest H can be found in the database maintained by Andrew Sutherland.

- Here is the code K0Finder (Java, bash, and maple are required).

Parameters include varpi_v, deltap, and A, for ϖ = 1/pi_r-varpi_v*10-5, δ'=deltap, and A=A.

- Here are some additional notes for the usage (in mpz.txt):

(1) For setting the parameter range of varpi_v, varpi_v<105/pi_r should always be enforced.

(2) Sometimes there is an addditional constraint δ=δ', you just need to add a line "deltap := delta;", after the definition of delta (See this file).

(3) Sometimes (deltap - delta) instead of (deltap - delta)/2 is used for calculating thetat (See this file).

(4) the solution can be verified using maple, but do not run maple at the same directory when the algorithm is running.

- Computation for some other (pi_r, delta_r) pairs:

(828, 172), i=1: k0=20419.
(348, 68), i=1: k0=5447.
(168, 48), i=2: k0=1783 (The Deligne-avoiding case).
(148, 33), i=1: k0=1466.
(140, 32), i=1: k0=1346.
(116, 30), i=1: k0=1007.
(108, 30), i=1: k0=962.
(280/3, 80/3), i=1: k0=873 for δ=δ'; k0=720, if (deltap - delta) instead of (deltap - delta)/2 is used for calculating thetat; k0=720, if without any additional constraints.
(600/7, 180/7), i=4: k0=632 (need some modifications on the code).

- Note: the k0 values in the table below might not be optimal, but they might be good starting points for saving some computational time in searching better values in similar pi_r and delta_r settings.

pi_r, delta_r30252015105
108902902902902901901
107889----888
106876----876
105864----863
104851----850
103838----838
102826----826
101813----813
100801801801801800800
99791----788
98777----776
97763----764
96753----751
95741----739
94728----727
93716----714
92704----703
91693----692
90681----680
89669----668
88658----656
87646----645
86635----634
85623----622
84612----610
83601----600
82590----589
81579----578
80568----566
79557----556
78546----544
77535----534
76524----523
75514514513513513512
74503----502
73493----492
72483----480
71472----471
70462----461
69452----450
68442----440
67432----430
66422----420
65412----410
64402----401
63393----390
62383----382
61374----372
60364----362
59355----353
58346----344
57337----335
56328----326
55319----317
54310----308
53302----298
52295----291
51284----282
50276275275274274272
49267----265
48259----256
47251----248
46243----240
45235----232
44227----224
43219----216
42211----209
41204----201
40197----194
39189----186
38182----179
37175----171
36168----164
35161----157
34154----150
33148----144
32141----137
31135----131
30129----124
29123----118
28117----112
27111----106
26105----100
2510099-96-94