On the error term in Weyl's law for Heisenberg manifolds
Wenguang Zhai (2008)
Acta Arithmetica
Similarity:
Wenguang Zhai (2008)
Acta Arithmetica
Similarity:
Kühleitner, M. (1992)
Acta Mathematica Universitatis Comenianae. New Series
Similarity:
Manfred Kühleitner, Werner Nowak (2006)
Open Mathematics
Similarity:
The arithmetic function ρ(n) counts the number of ways to write a positive integer n as a difference of two squares. Its average size is described by the Dirichlet summatory function Σn≤x ρ(n), and in particular by the error term R(x) in the corresponding asymptotics. This article provides a sharp lower bound as well as two mean-square results for R(x), which illustrates the close connection between ρ(n) and the number-of-divisors function d(n).
Kellner, Bernd C. (2009)
Integers
Similarity:
Aleksandar Ivić (2004)
Open Mathematics
Similarity:
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of . If with , then we obtain . We also show how our method of proof yields the bound , where T 1/5+ε≤G≪T, T
Broughan, Kevin A. (2001)
Journal of Integer Sequences [electronic only]
Similarity:
Spiro, Claudia A. (1985)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Panholzer, Alois, Prodinger, Helmut (2009)
Integers
Similarity:
Manfred Kühleitner, Werner Nowak (2013)
Open Mathematics
Similarity:
The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series of the form ζ 2(s)ζ(2s−1)ζ M(2s)H(s), where M is an arbitrary integer and H(s) has an Euler product which converges absolutely for R s > σ0, with some fixed σ0 < 1/2.
R. R. Hall, G. Tenenbaum (1986)
Compositio Mathematica
Similarity:
Kühleitner, Manfred (1998)
Mathematica Pannonica
Similarity:
Kühleitner, Manfred (1998)
Mathematica Pannonica
Similarity: