Summary

You searched for: Spectrum0=1/5,2/5,3/5,4/5

Your search produced 2 matches

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1

New Number: 4.66 |  AESZ: 300  |  Superseeker: -1616 -283183120  |  Hash: edc54887effd2ebcaa636dcc93baf0b7  

Degree: 4

\(\theta^4+2^{4} x\left(371\theta^4+862\theta^3+591\theta^2+160\theta+15\right)+2^{11} 5 x^{2}\left(224\theta^4+2069\theta^3+3277\theta^2+1363\theta+159\right)-2^{16} 5^{2} x^{3}\left(2089\theta^4+7500\theta^3+5533\theta^2+1500\theta+135\right)+2^{23} 5^{3} x^{4}(5\theta+1)(5\theta+2)(5\theta+3)(5\theta+4)\)

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Coefficients of the holomorphic solution: 1, -240, 378000, -941740800, 2908743037200, ...
--> OEIS
Normalized instanton numbers (n0=1): -1616, 265534, -283183120, 351860487150, -525536710386800, ... ; Common denominator:...

Discriminant

\((6400000z^2+6576z+1)(-1+320z)^2\)

Local exponents

≈\(-0.000842\) ≈\(-0.000186\)\(0\)\(s_2\)\(s_1\)\(\frac{ 1}{ 320}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 5}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 5}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 3}{ 5}\)
\(2\)\(2\)\(0\)\(2\)\(2\)\(4\)\(\frac{ 4}{ 5}\)

Note:

Sporadic Operator.

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2

New Number: 1.1 |  AESZ: 1  |  Superseeker: 575 63441275  |  Hash: c86f1c284d8c5119801c6ba1343172bb  

Degree: 1

\(\theta^4-5 x(5\theta+1)(5\theta+2)(5\theta+3)(5\theta+4)\)

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Coefficients of the holomorphic solution: 1, 120, 113400, 168168000, 305540235000, ...
--> OEIS
Normalized instanton numbers (n0=1): 575, 121850, 63441275, 48493506000, 45861177777525, ... ; Common denominator:...

Discriminant

\(1-3125z\)

Local exponents

\(0\)\(\frac{ 1}{ 3125}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 5}\)
\(0\)\(1\)\(\frac{ 2}{ 5}\)
\(0\)\(1\)\(\frac{ 3}{ 5}\)
\(0\)\(2\)\(\frac{ 4}{ 5}\)

Note:

A-incarnation: $X(5) \subset P^4$
B-incarnation: mirror quintic.
P. Candelas, X. de la Ossa, D. Green, L. Parkes,{\em An exactly soluble superconformal theory from a mirror pair of Calabi-Yau manifolds}, Phys. Lett. B 258 (1991), no.1-2, 118-126.

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