Summary

You searched for: inst=-150003/2

Your search produced exactly one match

1

New Number: 8.15 |  AESZ: 178  |  Superseeker: 18 9799/3  |  Hash: e748913f322a008ae5c350f96f1cd860  

Degree: 8

\(\theta^4-3 x(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+3^{3} x^{2}\left(217\theta^4+1732\theta^3+2441\theta^2+1418\theta+336\right)+2^{3} 3^{6} x^{3}\left(51\theta^4-306\theta^3-934\theta^2-717\theta-204\right)-2^{4} 3^{8} x^{4}\left(289\theta^4+578\theta^3-1310\theta^2-1599\theta-570\right)+2^{6} 3^{11} x^{5}\left(51\theta^4+510\theta^3+290\theta^2-29\theta-64\right)+2^{6} 3^{13} x^{6}\left(217\theta^4-864\theta^3-1453\theta^2-864\theta-156\right)-2^{9} 3^{16} x^{7}(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{12} 3^{20} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 378, 6552, 21546, ...
--> OEIS
Normalized instanton numbers (n0=1): 18, -423/2, 9799/3, -150003/2, 1914237, ... ; Common denominator:...

Discriminant

\((1728z^2-72z+1)(2187z^2-81z+1)(-1+1944z^2)^2\)

Local exponents

\(-\frac{ 1}{ 108}\sqrt{ 6}\)\(0\)\(\frac{ 1}{ 54}-\frac{ 1}{ 162}\sqrt{ 3}I\)\(\frac{ 1}{ 54}+\frac{ 1}{ 162}\sqrt{ 3}I\)\(\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I\)\(\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I\)\(\frac{ 1}{ 108}\sqrt{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

Hadamard product $d \ast g$. This operator has a second MUM-point at infinity. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{?})$.

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex