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Theta series of 28-dimensional unimodular lattice with no roots and with no parity vector of norm 4.
2

%I #17 Jan 29 2022 01:04:45

%S 1,0,0,2240,98280,1790208,19138560,141920640,805208040,3723722240,

%T 14651449344,50573436480,156717687840,443691198720,1162883174400,

%U 2851049534592,6596666916840,14509544394240,30507984568320

%N Theta series of 28-dimensional unimodular lattice with no roots and with no parity vector of norm 4.

%H R. Bacher and B. B. Venkov, <a href="https://www-fourier.univ-grenoble-alpes.fr/?q=fr/content/reseaux-entiers-unimodulaires-sans-racine-en-dimension-27-et-28">Réseaux entiers unimodulaires sans racine en dimension 27 et 28</a>, in Réseaux euclidiens, designs sphériques et formes modulaires, pp. 212-267, Enseignement Math., Geneva, 2001.

%F t3^28-56*t3^20*D8+280*t3^12*D8^2 where t3=theta_3(z) and D8=(theta_2(z)*theta_4(z))^4/16.

%t terms = 19; t3[z_] := EllipticTheta[3, 0, z]; D8[z_] := (EllipticTheta[2, 0, z]*EllipticTheta[4, 0, z])^4/16; s = t3[z]^28 - 56*t3[z]^20*D8[z] + 280*t3[z]^12*D8[z]^2 + O[z]^terms; CoefficientList[s, z] (* _Jean-François Alcover_, Jul 05 2017 *)

%Y Cf. A002519.

%K nonn,nice,easy

%O 0,4

%A _N. J. A. Sloane_

%E More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 04 2000