An application of Banach algebra techniques for multiplicative functions.
An arithmetic function arising from Carmichael’s conjecture
Let denote Euler’s totient function. A century-old conjecture of Carmichael asserts that for every , the equation has a solution . This suggests defining as the number of solutions to the equation . (So Carmichael’s conjecture asserts that always.) Results on are scattered throughout the literature. For example, Sierpiński conjectured, and Ford proved, that the range of contains every natural number . Also, the maximal order of has been investigated by Erdős and Pomerance. In...
An arithmetical mapping and applications to Ω-results for the Riemann zeta function
An asymptotic expansion.
An asymptotic formula for elements of a semigroup of integers
An Asymptotic Formula for the Variance of an Additive Function.
An Asymptotic Formula in the Theory of Numbers.
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 Series for an Additive Divisor Problem.
An Erdös-Kac theorem for integers without large prime factors
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 integral involving the remainder term in the Piltz divisor problem
An iteration problem involving the divisor function
An Omega theorem on differences of two squares.
An omega theorem on differences of two squares. II.
An ...-Theorem for an Error Term Related to the Sum-of-Divisors Function.
An ...-Theorem for Ramanujan's ...-Function.