A027638 - OEIS

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A027638

Order of 2^n X 2^n unitary group H_n acting on Siegel modular forms.

4, 96, 46080, 371589120, 48514675507200, 101643290713836748800, 3409750224676138896064512000, 1830483982118721406049481526345728000, 15723497752907010191583185709179507111362560000

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

OFFSET

0,1

REFERENCES

B. Runge, On Siegel modular forms I, J. Reine Angew. Math., 436 (1993), 57-85.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..39

Simon Burton, Elijah Durso-Sabina, and Natalie C. Brown, Genons, Double Covers and Fault-tolerant Clifford Gates, arXiv:2406.09951 [quant-ph], 2024. See p. 18.

B. Runge, Codes and Siegel modular forms, Discrete Math. 148 (1996), 175-204.

Index entries for sequences related to modular groups

FORMULA

a(n) = A003956(n)/2.

a(n) = 2^(n^2 + 2*n + 2) * Product_{j=1..n} (4^j - 1).

MAPLE

seq( 2^(n^2+2*n+2)*product(4^i -1, i=1..n), n=0..12);

MATHEMATICA

Table[2^(n^2+2n+2) Product[4^k-1, {k, n}], {n, 0, 10}] (* Harvey P. Dale, May 21 2018 *)

PROG

(Magma)

A027638:= func< n | n eq 0 select 4 else 2^(n^2+2*n+2)*(&*[4^j-1: j in [1..n]]) >;