A056945 -id:A056945

Search: a056945 -id:a056945

Displaying 1-2 of 2 results found.

page 1

A056946

Coefficients of J(0)*theta_3(z) where J(0) is sequence A056945.

+20
1

1, 2, 0, -4, 0, 12, 0, 32728, 196560, 262154, 0, 3734484, 16773120, 18345916, 0, 103029576, 398034000, 376741188, 0, 1334312620, 4629381120, 3937755904, 0, 10792611336, 34417656000, 26962933262, 0, 62783799320, 187489935360, 138065611740, 0, 287105506144, 814879774800

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Note a(4n)=A008408(n) gives theta series of Leech lattice. a(4n+2)=0. a(3)<0, apparently the only negative term. What are a(4n+1), a(4n+3)?

REFERENCES

Eichler and Zagier, The Theory of Jacobi Forms, Birkhauser, 1985.

LINKS

Table of n, a(n) for n=0..32.

FORMULA

(E_8*E_{4, 1}-60*E_{12, 1})*theta_3(z)

CROSSREFS

Cf. A008408, A056945.

KEYWORD

sign

AUTHOR

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 17 2000

STATUS

approved

A056950

Jacobi form of weight 12 and index 1 associated with a nonexistent Niemeier lattice of Coxeter number 11.

+10
0

1, 0, 0, 18, 226, 0, 0, 30800, 128172, 0, 0, 3697062, 9189144, 0, 0, 95514672, 188176158, 0, 0, 1143458294, 1959992760, 0, 0, 8506375824, 13292036472, 0, 0, 45760253096, 67075640896, 0, 0, 195396517152, 272568595860, 0, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

a(n)>=0, for n<1000.

REFERENCES

Eichler and Zagier, The Theory of Jacobi Forms, Birkhauser 1985.

LINKS

Table of n, a(n) for n=0..34.

FORMULA

E_8 * E_{4, 1} + (2*h - 60) * E_{12, 1} where h = 11.

a(n) = A055747(n) - 38*A003785(n). - Sean A. Irvine, May 18 2022

CROSSREFS

Cf. A003785, A055747, A056945.

KEYWORD

nonn

AUTHOR

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 18 2000

STATUS

approved

page 1

Search completed in 0.008 seconds