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Displaying 401 – 420 of 1970

A mean value related to the D. H. Lehmer problem and Kloosterman sums

Wenpeng Zhang, Zhaoxia Wu (2010)

Acta Arithmetica

A mean value theorem for the Dedekind Zeta-Function of a quadratic number field.

Jürgen G. Hinz (1979)

Monatshefte für Mathematik

A mean value theorem for the square of class number times regulator of quadratic extensions

Takashi Taniguchi (2008)

Annales de l’institut Fourier

Let $k$ be a number field. In this paper, we give a formula for the mean value of the square of class number times regulator for certain families of quadratic extensions of $k$ characterized by finitely many local conditions. We approach this by using the theory of the zeta function associated with the space of pairs of quaternion algebras. We also prove an asymptotic formula of the correlation coefficient for class number times regulator of certain families of quadratic extensions.

A mean value theorem of Bombieri's type

E. Fogels (1972)

Acta Arithmetica

A mean value theorem on differences of two k-th powers of numbers in residue classes.

Gerald Kuba (1991)

Manuscripta mathematica

A mean-square bound for the lattice discrepancy of bodies of rotation with flat points on the boundary

Werner Georg Nowak (2007)

Acta Arithmetica

A Mean-Value Theorem for Multiplicative Functions.

Karl-Heinz Indlekofer (1980)

Mathematische Zeitschrift

A measure-theoretic approach to the invariants of the Selberg class

J. Kaczorowski, A. Perelli (2008)

Acta Arithmetica

A Menon-type identity using Klee's function

Arya Chandran, Neha Elizabeth Thomas, K. Vishnu Namboothiri (2022)

Czechoslovak Mathematical Journal

Menon’s identity is a classical identity involving gcd sums and the Euler totient function $φ$ . A natural generalization of $φ$ is the Klee’s function $Φ_{s}$ . We derive a Menon-type identity using Klee’s function and a generalization of the gcd function. This identity generalizes an identity given by Y. Li and D. Kim (2017).