Compressed lattice sums arising from the Poisson equation

Boundary Value Problems

Table 1 PSLQ runs to recover minimal polynomials satisfied by $exp (8 π \sqrt{d} ϕ_{2} (1 / d, 1 / \sqrt{d}, d))$

d	m(d)	P	T	${log}_{10} M$	$\frac{{log}_{10} M}{m (d)}$
3	1	200	0.00
4	4	200	0.01	3.5230	0.8807
5	4	200	0.01	2.3222	0.5806
6	8	200	0.02	5.8061	0.7258
7	3	200	0.01	1.1461	0.3820
8	16	1,000	0.85	14.0644	0.8790
9	6	200	0.01	3.9187	0.6531
10	16	1,000	0.76	12.1262	0.7579
11	15	1,000	0.55	7.5230	0.5015
12	16	1,000	0.85	15.2686	0.9543
13	12	1,000	0.45	9.5690	0.7974
14	48	4,000	100.31	38.4539	0.8011
15	8	200	0.03	2.1139	0.2642
16	32	2,000	12.51	33.7985	1.0562
17	32	2,000	8.93	21.9952	0.6874
18	24	2,000	4.32	21.1366	0.8807
19	27	2,000	5.27	16.8591	0.6244
20	64	5,000	415.78	58.8250	0.9191
21	24	2,000	4.52	15.6374	0.6516
22	40	3,000	64.33	41.4566	1.0364
23	33	3,000	10.92	14.4705	0.4385
24	64	5,000	412.59	60.3300	0.9427
25	20	2,000	3.77	20.0766	1.0038
26	144	25,000	71,680.30	121.91	0.8466
27	27	2,000	5.70	18.9234	0.7009
28	48	4,000	131.29	58.4901	1.2185
29	84	6,000	1,375.38	60.0921	0.7154
30	64	5,000	557.29	56.9952	0.8906
31	45	4,000	38.89	19.8425	0.4409
33	40	4,000	81.42	32.1363	0.8034
34	128	21,300	45,993.71	123.9012	0.9680
35	72	12,000	1,179.43	41.3569	0.5744
36	96	12,000	95.3311	95.3311	0.9930
37	36	3,000	29.11	43.5933	1.2110
39	48	4,000	56.33	20.7849	0.4330
40	128	21,300		127.3572	0.9950

Here m(d) is the degree, P is the precision level in digits, T is the run time in seconds, and log₁₀M is the size in digits of the central coefficient. Degrees in bold were obtained by Andrew Mattingly.