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You searched for: Spectrum0=0,1/2,1

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1

New Number: 3.1.1 |  AESZ:  |  Superseeker:  |  Hash: 31acf361bebee650cbe6ec19f48bba9d  

Degree:

\(\theta^3-2^{3} 3 x(6\theta+5)(2\theta+1)(6\theta+1)\)

Maple   LaTex

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

Discriminant

\(1-1728z\)

Local exponents

\(0\)\(\frac{ 1}{ 1728}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 5}{ 6}\)
\(\)\(\)\(\)

Note:

Golyshev[11]/2, Golyshev[1].
Links?

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2

New Number: 3.1.2 |  AESZ:  |  Superseeker:  |  Hash: 30e7d091f57f3cdaa7996f96f226df67  

Degree:

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

Maple   LaTex

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

Discriminant

\(1-256z\)

Local exponents

\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(\)\(\)\(\)

Note:

Golyshev[12]/2,Golyshev[17]/4,Golyshev[2]

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3

New Number: 3.2.2 |  AESZ:  |  Superseeker:  |  Hash: 705aedd07e501ff2aea144d5c26c50fa  

Degree:

\(\theta^3-x(2\theta+1)(11\theta^2+11\theta+5)+5^{3} x^{2}\left((\theta+1)^3\right)\)

Maple   LaTex

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

Discriminant

\(1-22z+125z^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(\)\(\)\(\)\(\)

Note:

eta

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4

New Number: 3.2.1 |  AESZ:  |  Superseeker:  |  Hash: 9186bb2eb69ac43cd8c158eda22933db  

Degree:

\(\theta^3-3 x(2\theta+1)(3\theta^2+3\theta+1)-3^{3} x^{2}\left((\theta+1)^3\right)\)

Maple   LaTex

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

Discriminant

\(1-18z-27z^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(\)\(\)\(\)\(\)

Note:

zeta,Golyshev[9]

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5

New Number: 3.2.3 |  AESZ:  |  Superseeker:  |  Hash: 08d5c4b795dcba2e75ec97a85183eaf1  

Degree:

\(\theta^3-2^{2} x(2\theta+1)(3\theta^2+3\theta+1)+2^{4} x^{2}\left((\theta+1)^3\right)\)

Maple   LaTex

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

Discriminant

\(1-24z+16z^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(\)\(\)\(\)\(\)

Note:

eps,Golyshev[8]

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6

New Number: 3.1.3 |  AESZ:  |  Superseeker:  |  Hash: 534f489d40d8c0abbbc975d6bf414480  

Degree:

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

Maple   LaTex

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

Discriminant

\(1-108z\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(\)\(\)\(\)

Note:

Golyshev[13]/2,Golyshev[16]/3,Golyshev[3]

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7

New Number: 3.1.4 |  AESZ:  |  Superseeker:  |  Hash: 0ea09490a9b355bb9c0dbd9fc85d10b1  

Degree:

\(\theta^3-2^{3} x\left((2\theta+1)^3\right)\)

Maple   LaTex

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

Discriminant

\(1-64z\)

Local exponents

\(0\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(\)\(\)\(\)

Note:

Golyshev[14]/2,Golyshev[4]

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8

New Number: 3.2.12 |  AESZ:  |  Superseeker:  |  Hash: 4c9d5ced5d0bd4994da62251213be600  

Degree:

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

Maple   LaTex

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

Discriminant

\(-(4z+1)(16z-1)\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(\frac{ 1}{ 2}\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 4}\)
\(\)\(\)\(\)\(\)

Note:

Afunc[18]

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9

New Number: 3.2.13 |  AESZ:  |  Superseeker:  |  Hash: 28f660387aee808cd7c7b7af80a7da69  

Degree:

\(\theta^3-x(2\theta+1)(13\theta^2+13\theta+4)-3 x^{2}(3\theta+2)(3\theta+4)(\theta+1)\)

Maple   LaTex

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

Discriminant

\(-(z+1)(27z-1)\)

Local exponents

\(-1\)\(0\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(\frac{ 1}{ 2}\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(1\)\(\frac{ 4}{ 3}\)
\(\)\(\)\(\)\(\)

Note:

Afunc[26],Golyshev[7]

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10

New Number: 3.2.16 |  AESZ:  |  Superseeker:  |  Hash: b84ae0ed53f62f243b74840ba8ccff4e  

Degree:

\(\theta^3-2 x(2\theta+1)(11\theta^2+11\theta+3)-2^{2} x^{2}(2\theta+3)(2\theta+1)(\theta+1)\)

Maple   LaTex

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

Discriminant

\(1-44z-16z^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(\)\(\)\(\)\(\)

Note:

Golyshev[15]/2,Golyshev[5]

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11

New Number: 3.2.4 |  AESZ:  |  Superseeker:  |  Hash: 372efeeaa62eb6e55239f731e7ac1642  

Degree:

\(\theta^3-x(2\theta+1)(7\theta^2+7\theta+3)+3^{4} x^{2}\left((\theta+1)^3\right)\)

Maple   LaTex

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

Discriminant

\(1-14z+81z^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(\)\(\)\(\)\(\)

Note:

delta

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12

New Number: 3.2.5 |  AESZ:  |  Superseeker:  |  Hash: c99003e60b536d9d793b3569f517b1c8  

Degree:

\(\theta^3-2 x(2\theta+1)(5\theta^2+5\theta+2)+2^{6} x^{2}\left((\theta+1)^3\right)\)

Maple   LaTex

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

Discriminant

\((16z-1)(4z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(\)\(\)\(\)\(\)

Note:

alpha

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13

New Number: 3.2.6 |  AESZ:  |  Superseeker:  |  Hash: f29acfc249c8fdfff79fcf325768c5f6  

Degree:

\(\theta^3-x(2\theta+1)(17\theta^2+17\theta+5)+x^{2}\left((\theta+1)^3\right)\)

Maple   LaTex

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

Discriminant

\(1-34z+z^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(\)\(\)\(\)\(\)

Note:

gamma,Golyshev[6]

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14

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

Degree:

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

Maple   LaTex

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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15

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

Degree:

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

Maple   LaTex

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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16

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

Degree:

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

Maple   LaTex

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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17

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

Degree:

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

Maple   LaTex

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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