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- W65003912 abstract "Kummer considered cyclotomy for a composite modulus n and defined the periods by $$n_k = sumlimits_{v = 0}^{f - 1} {zeta _n^{kq^upsilon } } knot equiv q^j (bmod n),0 < j < phi (n)$$where ζn=exp(2πi/n) and f=t(n) is the order of q modulo n. He stated that, except when all the η's vanish, they satisfy an irreducible monic period equation with integer coefficients of degree ϕ(n)/t(n). Soon thereafter Fuchs gave a necessary and sufficient condition for the vanishing of the η's, namely: nk=0 if and only if t(n)=pt(n/p) for some prime p dividing n. A modern proof for a generalized period was recently given by R.J. Evans." @default.
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- W65003912 date "1981-01-01" @default.
- W65003912 modified "2023-09-24" @default.
- W65003912 title "Cyclotomy for non-squarefree modul I" @default.
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- W65003912 doi "https://doi.org/10.1007/bfb0096468" @default.
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