1,1

In this paper it is proved, that for every prime number p, the set of cyclic p-roots in C^p is finite. Moreover the number of cyclic p-roots counted with multiplicity is equal to (2p-2)!/(p-1)!^2. In particular, the number of complex circulant Hadamard matrices of size p, with diagonal entries equal to 1, is less or equal to (2p-2)!/(p-1)!^2.

Uffe Haagerup, Cyclic p-roots of prime lengths p and related complex Hadamard matrices, Mar 19, 2008.

a(n) = (2*p_n - 2)!/(p_n - 1)!^2 where p_n = prime(n) = A000040(n). a(n) = A000142(2*A000040(n)-2)/((A000142(A000040(n)-1)^2).

Cf. A000040, A000142.

Sequence in context: A091458 A087331 A097419 this_sequence A030242 A037293 A129785

Adjacent sequences: A136265 A136266 A136267 this_sequence A136269 A136270 A136271

easy,more,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 18 2008