OFFSET
-1,2
COMMENTS
On page 2 of Zagier "Traces of Singular Moduli" he writes "On the other hand, we define a (meromorphic) modular form of weight 3/2 by the formula g(tau) = theta_1(tau)*E_4(4*tau)/eta(4*tau)^6 = q^{-1} - 2 + 248q^3 - 492q^4 + 4119q^7 - 7256q^8 + ..., (3)". - Michael Somos, Jul 04 2014
In Mathoverflow question 158075 Piezas writes "Zagier defines the modular form of weight 3/2, g(tau) = (eta^2(tau)/eta(2*tau))*(E_4(4*tau)/eta^6(4*tau)) = theta_4(tau)*eta^2(4*tau)*cbroot(j(4*tau)) which has the nice q-expansion (A027652, negated terms),". - Michael Somos, Jul 04 2014
REFERENCES
M. Kaneko, Fourier coefficients of the elliptic modular function j(tau) (in Japanese), Rokko Lectures in Mathematics 10, Dept. Math., Faculty of Science, Kobe University, Rokko, Kobe, Japan, 2001.
LINKS
Seiichi Manyama, Table of n, a(n) for n = -1..10000 (terms -1..2000 from N. J. A. Sloane)
M. Kaneko, The Fourier coefficients and the singular moduli of the elliptic modular function j(tau), Memoirs Faculty Engin. Sci., Kyoto Inst. Technology, 44 (March 1996), pp. 1-5.
T. Piezas, Monstrous Moonshine for Thompson group Th?
D. Zagier, Traces of Singular Moduli
EXAMPLE
G.f. = -1/q + 2 - 248*q^3 + 492*q^4 - 4119*q^7 + 7256*q^8 - 33512*q^11 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (-1/q) EllipticTheta[ 4, 0, q] QPochhammer[ q^4]^2 (QPochhammer[ q^4, q^8]^8 + 256 q^4 QPochhammer[ q^4, q^8]^-16), {q, 0, n}]; (* Michael Somos, Jul 19 2015 *)
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
Entry revised by N. J. A. Sloane, Jul 25 2006
STATUS
approved