I am looking for a reference giving the decomposition of a prime p in the maximal real subfield of a cyclotomic number field Q(zeta_m). Something along these lines: If p is a prime not dividing m, then let f be the smallest positive integer such that p to the f is congruent to 1 or -1 modulo m. Write f.g=phi(m)/2. Then (p) splits into g different prime ideals of norm f (plus what happens if p divides m).
Thong Nguyen Quang Do
Dear Pieter,
I think you can find your answer in the book of Daniel A. Marcus, "Number Fields", Springer Universitex, 19977, chapter 4, exercise 12, p.118 (see also ex. 14)
Best, T. NQD
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