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Search: id:A035315
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| A035315 |
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Fourier coefficients of T_{10}. |
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+0
1
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| 1, 264, 8244, 139520, 1672290, 15872256, 126745880, 884100096, 5525046495, 31498809600, 166049246340, 817866616320, 3794952949854, 16699329285120, 70071039813240, 281650911606784, 1088671630120515, 4060062852952320
(list; graph; listen)
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OFFSET
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-1,2
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COMMENT
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T_{10} is the unique weight = -8 normalized meromorphic modular form for SL(2,Z) with all poles at infinity.
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REFERENCES
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C. L. Siegel, Advanced Analytic Number Theory,Tata Institute of Fundamental Research, Bombay, 1980, pp. 249-268.
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LINKS
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Borcherds, Richard E., Automorphic forms with singularities on Grassmannians, Invent. Math. 132 (1998), 491-562.
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FORMULA
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G.f. = G_4/Delta (in Siegel's notation.)
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EXAMPLE
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T_{10} = 1/q + 264 + 8244 q + ....
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PROGRAM
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(PARI) {a(n)=if(n<-1, 0, n++; polcoeff( sum(k=1, n, 240*sigma(k, 3)*x^k, 1+x*O(x^n))/eta(x+x*O(x^n))^24, n))} /* Michael Somos Apr 12 2005 */
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CROSSREFS
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Sequence in context: A092724 A112069 A022043 this_sequence A107507 A013974 A145639
Adjacent sequences: A035312 A035313 A035314 this_sequence A035316 A035317 A035318
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KEYWORD
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easy,nonn
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AUTHOR
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Barry Brent (barryb(AT)primenet.com)
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