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On Lehmer's problem and Dedekind sums

Xiaowei Pan, Wenpeng Zhang (2011)

Czechoslovak Mathematical Journal

Let p be an odd prime and c a fixed integer with ( c , p ) = 1 . For each integer a with 1 a p - 1 , it is clear that there exists one and only one b with 0 b p - 1 such that a b c (mod p ). Let N ( c , p ) denote the number of all solutions of the congruence equation a b c (mod p ) for 1 a , b p - 1 in which a and b ¯ are of opposite parity, where b ¯ is defined by the congruence equation b b ¯ 1 ( mod p ) . The main purpose of this paper is to use the properties of Dedekind sums and the mean value theorem for Dirichlet L -functions to study the hybrid mean value problem involving...

On the mean value of Dedekind sum weighted by the quadratic Gauss sum

Tingting Wang, Wenpeng Zhang (2013)

Czechoslovak Mathematical Journal

Various properties of classical Dedekind sums S ( h , q ) have been investigated by many authors. For example, Wenpeng Zhang, On the mean values of Dedekind sums, J. Théor. Nombres Bordx, 8 (1996), 429–442, studied the asymptotic behavior of the mean value of Dedekind sums, and H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs No. 16, The Mathematical Association of America, Washington, D.C., 1972, studied the related properties. In this paper, we use the algebraic method to...

On the mean values of Dedekind sums

Wenpeng Zhang (1996)

Journal de théorie des nombres de Bordeaux

In this paper we study the asymptotic behavior of the mean value of Dedekind sums, and give a sharper asymptotic formula.

One special class of modular forms and group representations

Galina V. Voskresenskaya (1999)

Journal de théorie des nombres de Bordeaux

In this article we consider one special class of modular forms which are products of Dedekind η -functions and the relationships between these functions and representations of finite groups.

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