OFFSET
-1,2
COMMENTS
T_{10} is the unique weight = -8 normalized meromorphic modular form for SL(2,Z) with all poles at infinity.
REFERENCES
C. L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1980, pp. 249-268.
LINKS
Seiichi Manyama, Table of n, a(n) for n = -1..1000
Borcherds, Richard E., Automorphic forms with singularities on Grassmannians, Invent. Math. 132 (1998), 491-562.
FORMULA
G.f.: G_4/Delta (in Siegel's notation.)
a(n) ~ exp(4*Pi*sqrt(n)) / (sqrt(2) * n^(19/4)). - Vaclav Kotesovec, Oct 04 2020
EXAMPLE
T_{10} = 1/q + 264 + 8244 q + ....
PROG
(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 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry Brent (barryb(AT)primenet.com)
STATUS
approved