Summary

You searched for: inst=-16

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1

New Number: 4.35 |  AESZ:  |  Superseeker: -16 -1744  |  Hash: cd392ce4c33f242f5d17e59976d0ea4f  

Degree: 4

\(\theta^4-2^{4} x\left(23\theta^4+14\theta^3+13\theta^2+6\theta+1\right)+2^{11} x^{2}\theta(21\theta^3+24\theta^2+18\theta+4)-2^{16} x^{3}(2\theta+1)(10\theta^3+7\theta^2-5\theta-4)-2^{23} x^{4}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 16, 912, 67840, 5839120, ...
--> OEIS
Normalized instanton numbers (n0=1): -16, -106, -1744, -29526, -644016, ... ; Common denominator:...

Discriminant

\(-(16z+1)(128z-1)^3\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(\frac{ 3}{ 2}\)\(1\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Operator equivalent to 3.34, equivalent to
AESZ 107 $=d \ast d$.

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2

New Number: 5.99 |  AESZ: 342  |  Superseeker: -4 3856/9  |  Hash: 009a00efdd065ef9ea58db999d777786  

Degree: 5

\(\theta^4+2 x\left(50\theta^4+64\theta^3+52\theta^2+20\theta+3\right)+2^{2} 3 x^{2}\left(380\theta^4+992\theta^3+1166\theta^2+612\theta+117\right)+2^{2} 3^{2} x^{3}\left(2140\theta^4+5832\theta^3+5651\theta^2+2349\theta+360\right)+2^{4} 3^{6} x^{4}(2\theta+1)(20\theta^3+42\theta^2+35\theta+11)+2^{6} 3^{7} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, -6, 54, 660, -69930, ...
--> OEIS
Normalized instanton numbers (n0=1): -4, -16, 3856/9, -3864, -20784, ... ; Common denominator:...

Discriminant

\((3888z^3+2592z^2+76z+1)(1+12z)^2\)

Local exponents

≈\(-0.636595\)\(-\frac{ 1}{ 12}\) ≈\(-0.015036-0.01334I\) ≈\(-0.015036+0.01334I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)
\(1\)\(3\)\(1\)\(1\)\(0\)\(1\)
\(2\)\(4\)\(2\)\(2\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.99" from ...

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3

New Number: 5.9 |  AESZ: 56  |  Superseeker: -16 -3280  |  Hash: 58a7f24bf18cb98b526885069667f9f0  

Degree: 5

\(\theta^4-2^{4} x\left(22\theta^4+8\theta^3+9\theta^2+5\theta+1\right)+2^{9} x^{2}\left(94\theta^4+88\theta^3+97\theta^2+45\theta+8\right)-2^{14} x^{3}\left(194\theta^4+336\theta^3+371\theta^2+195\theta+41\right)+2^{19} 3 x^{4}\left(64\theta^4+176\theta^3+217\theta^2+129\theta+30\right)-2^{27} 3^{2} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 16, 464, 17152, 725776, ...
--> OEIS
Normalized instanton numbers (n0=1): -16, -178, -3280, -76197, -2046896, ... ; Common denominator:...

Discriminant

\(-(-1+32z)(96z-1)^2(64z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 96}\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(4\)\(1\)\(2\)\(1\)

Note:

There is a second MUM-point hiding at infinity, corresponding to Operator...

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