Summary

You searched for: Spectrum0=1,2,3

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1

New Number: 3.4.1 |  AESZ:  |  Superseeker:  |  Hash: c059a405cf4b3046b11c01197518c49c  

Degree:

\(\theta^3-5 x(2\theta+1)(26\theta^2+26\theta+5)+x^{2}(\theta+1)(774\theta^2+1548\theta+823)-2 193 x^{3}(2\theta+3)(\theta+2)(\theta+1)+257 x^{4}(\theta+3)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: , ...
--> OEIS
Normalized instanton numbers (n0=1): , ... ; Common denominator:...

Discriminant

\((257z-1)(z-1)^3\)

Local exponents

\(0\)\(\frac{ 1}{ 257}\)\(1\)\(\infty\)
\(0\)\(0\)\(-\frac{ 3}{ 4}\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(-\frac{ 1}{ 4}\)\(3\)
\(\)\(\)\(\)\(\)

Note:

Afunc[75]

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2

New Number: 3.4.2 |  AESZ:  |  Superseeker:  |  Hash: 7ed881d5c6011878b75d16414ccae150  

Degree:

\(\theta^3-x(2\theta+1)(866\theta^2+866\theta+121)+x^{2}(\theta+1)(5190\theta^2+10380\theta+5431)-2 1297 x^{3}(2\theta+3)(\theta+2)(\theta+1)+7 13 19 x^{4}(\theta+3)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: , ...
--> OEIS
Normalized instanton numbers (n0=1): , ... ; Common denominator:...

Discriminant

\((1729z-1)(z-1)^3\)

Local exponents

\(0\)\(\frac{ 1}{ 1729}\)\(1\)\(\infty\)
\(0\)\(0\)\(-\frac{ 5}{ 6}\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(-\frac{ 1}{ 6}\)\(3\)
\(\)\(\)\(\)\(\)

Note:

Afunc[85]

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3

New Number: 3.4.3 |  AESZ:  |  Superseeker:  |  Hash: 8fae5b30dfb4b545adfd8cf16005fd33  

Degree:

\(\theta^3-x(2\theta+1)(56\theta^2+56\theta+13)+5 x^{2}(\theta+1)(66\theta^2+132\theta+71)-2^{2} 41 x^{3}(2\theta+3)(\theta+2)(\theta+1)+109 x^{4}(\theta+3)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: , ...
--> OEIS
Normalized instanton numbers (n0=1): , ... ; Common denominator:...

Discriminant

\((109z-1)(z-1)^3\)

Local exponents

\(0\)\(\frac{ 1}{ 109}\)\(1\)\(\infty\)
\(0\)\(0\)\(-\frac{ 2}{ 3}\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(-\frac{ 1}{ 3}\)\(3\)
\(\)\(\)\(\)\(\)

Note:

Afunc[117],Afunc[90]

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4

New Number: 3.4.4 |  AESZ:  |  Superseeker:  |  Hash: 35a2fcb3c8a3c4d7ee29cbf9ba85f7ba  

Degree:

\(5^{4} \theta^3-2 5^{3} x(2\theta+1)(17\theta^2+17\theta+6)-2^{3} 5^{2} 7 x^{2}(\theta+1)(11\theta^2+22\theta+12)-2 3^{2} 5 7 x^{3}(2\theta+3)(\theta+2)(\theta+1)-2^{5} 47 x^{4}(\theta+3)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: , ...
--> OEIS
Normalized instanton numbers (n0=1): , ... ; Common denominator:...

Discriminant

\(-(8z+5)(188z^3+40z^2+1900z-125)\)

Local exponents

\(-\frac{ 5}{ 8}\)\(0\)\(s_1\)\(s_3\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(2\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)
\(\)\(\)\(\)\(\)\(\)\(\)

Note:

Golyshev[10]

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