An asymptotic formula in the theory of numbers
An Asymptotic Formula in the Theory of Numbers. II:
An Asymptotic Formula in the Theory of Numbers. III.
An asymptotic formula related to the divisors of the quaternary quadratic form
Let d(n) stand for the Dirichlet divisor function. We give an asymptotic formula for with the help of the circle method.
An asymptotic inequality concerning primes in contours for the case of quadratic number fields
An Asymptotic Series for an Additive Divisor Problem.
An average form of Artin's conjecture
An elementary method in prime number theory
An Erdös-Kac theorem for integers without large prime factors
An example for Gelfand's theory of commutative Banach algebras
An example in Beurling's theory of generalised primes
We prove some connections between the growth of a function and its Mellin transform and apply these to study an explicit example in the theory of Beurling primes. The example has its generalised Chebyshev function given by [x]-1, and associated zeta function ζ₀(s) given via , where ζ is Riemann’s zeta function. We study the behaviour of the corresponding Beurling integer counting function N(x), producing O- and Ω- results for the ’error’ term. These are strongly influenced by the size of ζ(s) near...
An example in Beurling's theory of primes
An explicit estimate for zeros of Dedekind zeta functions
An explicit Mertens' type inequality for arithmetic progressions.
An identity involving Dedekind sums and generalized Kloosterman sums
The various properties of classical Dedekind sums have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums . The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of...
An Improved Bound for Prime Solutions of Some Ternary Equations.
An inequality for the class number.
An integral involving the remainder term in the Piltz divisor problem
An interval result for the number field v(x,y) function.
An iteration problem involving the divisor function