1 Ju l 2 00 7 On some power sum problems of Montgomery
نویسنده
چکیده
We use an estimate for character sums over finite fields of Katz to solve open problems of Montgomery and Turán. Let h ≥ 2 be an integer. We prove that inf |z k |=1 max ν=1,...,n h | n k=1 z ν k | ≤ (h − 1 + o(1)) √ n. This gives the right order of magnitude for the quantity and improves on a bound of Erd˝ os-Renyi by a factor of the order √ log n.
منابع مشابه
0 Ju l 2 00 6 Explicit solutions to certain inf max problems from Turán power sum theory
k=1 z k ∣ ∣ ∣ ∣ ∣ = √ n (i = 2, . . . , n − 1) when n ≥ 3 is a prime power. We give explicit constructions of n-tuples (z1, . . . , zn) which we prove are global minima for these problems. These are two of the few times in Turán power sum theory where solutions in the inf max problem can be explicitly calculated.
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