65 research outputs found
Evaluating Prime Power Gauss and Jacobi Sums
We show that for any mod characters, the
Jacobi sum,
has a simple evaluation when is sufficiently large (for if
). As part of the proof we give a simple evaluation of the mod
Gauss sums when
Waring's number for large subgroups of double-struck Z_p
Let p be a prime, Z_p be the finite field in p elements, k be a positive integer, and A be the multiplicative subgroup of nonzero k-th powers in Z_p. The goal of this paper is to determine, for a given positive integer s, a value t_s such that if |A| ≫ t_s then every element of Z_p is a sum of s k-th powers. We obtain t_4 = p^{\frac{22}{39} + \in}, t_5 = p^{\frac{15}{29} + \in} and for s s ≥ 6, t_s = p^{\frac{9s+45}{29s+33} + \in}. For s ≥ 24 further improvements are made, such as t_32 = p^{\frac{5}{16} + \in} and t_128 = p^{\frac{1}{4}}
SUBJECTIVE RATINGS OF MEDICATION STRENGTH OVER 6 MONTHS IN ELDERLY SUBJECTS WITH MODERATE OR SEVERE INSOMNIA TREATED WITH LEMBOREXANT
LONG-TERM PERCEPTION OF MEDICATION EFFECTIVENESS IN ELDERLY SUBJECTS WITH INSOMNIA RECEIVING LEMBOREXANT FOR UP TO 12 MONTHS
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