A generalization of a theorem by Cheo and Yien concerning digital sums.
A generalization of a theorem of Lekkerkerker to Ostrowski's decomposition of natural numbers
A generalization of Atkinson's formula to L-functions
A generalization of Bombieri's prime number theorem to algebraic number fields
A generalization of Pillai's arithmetical function involving regular convolutions
A generalization of the Buchstab equation.
A generalization of the Goldbach-Vinogradov theorem
A higher rank Selberg sieve and applications
We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings.
A hybrid mean value of the Dedekind sums
The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.
A hybrid mean value related to certain Hardy sums and Kloosterman sums
The main purpose of this paper is using the mean value formula of Dirichlet L-functions and the analytic methods to study a hybrid mean value problem related to certain Hardy sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.
A hybrid mean value related to Dedekind sums
The main purpose of this paper is to study a hybrid mean value problem related to the Dedekind sums by using estimates of character sums and analytic methods.
A hybrid of theorems of Goldbach and Piatetski-Shapiro
A Large Sieve Density Estimate near ?= 1.
A larger GL 2 large sieve in the level aspect
In this paper we study the orthogonality of Fourier coefficients of holomorphic cusp forms in the sense of large sieve inequality. We investigate the family of GL 2 cusp forms modular with respect to the congruence subgroups Γ1(q), with additional averaging over the levels q ∼ Q. We obtain the orthogonality in the range N ≪ Q 2−δ for any δ > 0, where N is the length of linear forms in the large sieve.
A larger sieve
A local Turán-Kubilius inequality
A lower bound for the error term in Weyl’s law for certain Heisenberg manifolds, II
This article is concerned with estimations from below for the remainder term in Weyl’s law for the spectral counting function of certain rational (2ℓ + 1)-dimensional Heisenberg manifolds. Concentrating on the case of odd ℓ, it continues the work done in part I [21] which dealt with even ℓ.
A lower bound on the number of finite simple groups.
A lower bound theorem in Fq[x].
A mean value related to the D. H. Lehmer problem and Kloosterman sums