On a Problem of D. H. Lehmer
Tóm tắt
The main purpose of this paper is to use the Fourier expansion for character sums and
the mean value theorem of Dirichlet L–functions to study the asymptotic property of the difference
between a D. H. Lehmer number and its inverse modulo p (an odd prime). A interesting mean square
value formula is also given.
Tài liệu tham khảo
Zhang, W. P.: On the difference between an integer and its inverse modulo n. Journal of Number Theory, 52, 1–6 (1995)
Zhang, W. P.: On the difference between an integer and its inverse modulo n (II). Science in China (Series A), 46, 229–238 (2003)
Richard, K. G.: Unsolved Problems in Number Theory, Springer-Verlag, 1981
Zhang, W. P.: On the difference between a D. H. Lehmer number and its inverse modulo q. Acta Arithmetica, LXVIII(3), 255–263 (1994)
Pólya, G.: Über die Verteilung der quadratishen Reste und Nichtreste. Gottinger Nachrichten, 21–29 (1918)
Funakura, Takeo: On Kronecker’s limit formula for Dirichlet series with periodic coefficients. Acta Arithmetica, 55, 59–73 (1990)
Apostol, T. M.: Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976