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secondary 11l05

Glasgow Mathematical Journal (1)

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GENERALIZED D. H. LEHMER PROBLEM OVER SHORT INTERVALS
PING XI, YUAN YI
Journal:

Glasgow Mathematical Journal / Volume 53 / Issue 2 / May 2011

Published online by Cambridge University Press:

13 December 2010, pp. 293-299

Print publication:

May 2011
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Let n ≥ 2 be a fixed positive integer, q ≥ 3 and c, ℓ be integers with (nc, q)=1 and ℓ|n. Suppose and consist of consecutive integers which are coprime to q. We define the cardinality of a set: The main purpose of this paper is to use the estimates of Gauss sums and Kloosterman sums to study the asymptotic properties of N(, , c, n, ℓ; q), and to give an interesting asymptotic formula for it.