Lehmer's Semi-symmetric Cyclotomic Sums
نویسندگان
چکیده
At the 1991 West Coast Number Theory Conference, Emma Lehmer asked for proofs of the formulas on semi-symmetric cyclotomic sums that appeared without proof in D. H. Lehmer's last notebook. This note is the result. Furthermore, we show how to determine signs which Lehmer had left ambiguous. Classical cyclotomy defined the cyclotomic classes of degree e and prime conductor p = ef + 1 to be (1) C (g) j = {g where g is any primitive root mod p. Here C (g) 0 contains the eth-power residues, but, as the notation emphasizes, the indexing of the other classes depends upon the choice of g. If g ∈ C
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