[seqfan] Re: Sum over tangents

Richard J. Mathar mathar at mpia-hd.mpg.de
Fri Apr 26 14:09:00 CEST 2013

http://list.seqfan.eu/pipermail/seqfan/2013-April/011083.html says

cgr> A086227 is defined as "a(n)=1/(4i)*sum( i^k*tan(k*Pi/4/n)) where 1<=k<=4n
cgr> and (k,n)=1" with no further comment. But it seems that the absolute value
cgr> of this sequence gives the class number for Q(sqrt(-4*n^2)). Is this true?
cgr> What is the connection between these definitions?

These might be related:

J. H. Conway, C. Radin, L. Sadun,
On angles whose squared trigonometric functions are rational
Discr. Comput. Geom. 22 (1999) 321-332

See Corollary 5.2 in
B. C. Berndt, A. Zaharescu,
Finite trigonometric sums and class numbers
doi: 10.1007/s00208-004-0559-5
Math. Ann. 330 (2004) 551-575

and perhaps

More information about the SeqFan mailing list