논문KCI 등재
D. H. Lehmer problem over half intervals
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Let q≥3 be an odd integer and a be an integer coprime to q. Denote by N(a,q) the number of pairs of integers b,c with bc ≡ a (mod q), 1≤b,c≤{q-1}/{2} and with b,c having different parity. The main purpose of this paper is to study the sum ∑'^q_(a=1)(N(a,q)-Φ(q)/8)^2 and obtain a sharp asymptotic formula.
Abstract
Let q≥3 be an odd integer and a be an integer coprime to q. Denote by N(a,q) the number of pairs of integers b,c with bc ≡ a (mod q), 1≤b,c≤{q-1}/{2} and with b,c having different parity. The main purpose of this paper is to study the sum ∑'^q_(a=1)(N(a,q)-Φ(q)/8)^2 and obtain a sharp asymptotic formula.
참고문헌 (6)
- R. K. Guy, "Unsolved Problems in Number Theory, Second edition. Problem Books in Mathematics. Unsolved Problems in Intuitive Mathematics, I" (1994), Springer-Verlag
- W. Zhang, "A problem of D. H. Lehmer and its generalization. II", Compositio Math., 91(1), pp.47~56 (1994)
- W. Zhang, "On the mean values of Dedekind sums", J. Theor. Nombres Bordeaux, 8(2), pp.429~442 (1996)
- W. Zhang, "A problem of D. H. Lehmer and its mean square value formula", Japan. J. Math., 29(1), pp.109~116 (2003)
- W. Zhang, "A problem of D. H. Lehmer and its mean square value formula", J. Number Theory, 103(2), pp.197~213 (2003)
- X. Zhefeng, "On a problem of D. H. Lehmer over short intervals", J. Math. Anal. Appl., 320(2), pp.756~770 (2006)
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