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Search: id:A027640
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| A027640 |
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Poincare series for ring of modular forms of genus 2. |
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+0
3
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| 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 3, 0, 2, 0, 4, 0, 4, 0, 5, 0, 6, 0, 8, 0, 7, 0, 10, 0, 11, 0, 12, 0, 14, 1, 17, 0, 16, 1, 21, 1, 22, 1, 24, 2, 27, 3, 31, 2, 31, 4, 37, 4, 39, 5, 42, 6, 46, 8, 52, 7, 52, 10, 60, 11, 63, 12, 67, 14
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OFFSET
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0,11
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COMMENT
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a(k) for k>0 is the dimension of the space of Siegel modular forms of genus 2 and weight k (for the full modular group Gamma_2). [From Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009]
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REFERENCES
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J. Igusa, On Siegel modular forms of genus 2 (II), Amer. J. Math., 86 (1964), 392-412, esp. p. 402.
B. Runge, On Siegel modular forms I, J. Reine Angew. Math., 436 (1993), 57-85.
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MAPLE
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(1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12));
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MATHEMATICA
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Table[SeriesCoefficient[Series[(1+t^(35))/((1-t^4) (1-t^6)(1-t^(10)) (1-t^(12))), {t, 0, 100}], i], {i, 0, 100}] [From Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009]
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CROSSREFS
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C.f. A165685 for the corresponding dimension of the space of cusp forms. [From Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009]
Sequence in context: A128144 A128145 A128143 this_sequence A127460 A154109 A011374
Adjacent sequences: A027637 A027638 A027639 this_sequence A027641 A027642 A027643
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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