On Differences and sums of Integers, II
On differences of two squares
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).
On difference-sequences
On differential operators attached to certain representations of classical groups.
On dihedral algebraic function fields
On diophantine equations involving sums of powers with quadratic characters as coefficients, I
On diophantine equations involving sums of powers with quadratic characters as coefficients, II
On Diophantine quintuples
On Dirchlet's series satisfying Riemann's functional equation.
On Dirichlet characters of polynomials
On Dirichlet convolution method.
On Dirichlet series and Hecke triangle groups of infinite volume
On Dirichlet Series and Petersson Products for Siegel Modular Forms
We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree and weight has meromorphic continuation to . Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight may be expressed in terms of the residue at of the associated Dirichlet series.
On Dirichlet series associated with cubic Gauss sums.
On Dirichlet's theorem concerning diophantine approximation
On discrete mean values of Dirichlet -functions
Let be a nonprincipal Dirichlet character modulo a prime number and let . Define the mean value We give an identity for which, in particular, shows that for fixed and .
On discriminants and indices of integers of an algebraic number field.
On disjoint arithmetic progressions
On Dispersion and Markov Constants.
On distinguished representations.