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On the r-free values of the polynomial x2 + y2 + z2 + k
Let k be a fixed integer. We study the asymptotic formula of R ( H,r,k ), which is the number of positive integer solutions 1 ⩽ x, y, z ⩽ H such that...
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Consecutive square-free values of the type x2 + y2 + z2 + k, x2 + y2 + z2 + k + 1
We show that for any given integer k there exist infinitely many consecutive square-free numbers of the type x 2 + y 2 + z 2 + k, x 2 + y 2 + z 2 + k + 1....
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Some novel identities for analogues of Dedekind sums, Hurwitz zeta-function and general Kloosterman sum
We discuss two hybrid mean value problems by using the properties of Dirichlet L -functions. The first one is involving a new sum analogue of Dedekind...
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On Ramanujan Sums over a Dedekind Domain with Finite Norm Property
In this paper, we consider Ramanujan’s sums over arbitrary Dedekind domain with finite norm property. We define the Ramanujan’s sums η ( a , A ) and η ( B , A ...
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On the Sixth Power Mean of the Two-term Exponential Sums
The main purpose of this article is to study the calculating problem of the sixth power mean of the two-term exponential sums, and give an...
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Bilinear forms with trace functions over arbitrary sets and applications to Sato-Tate
We prove non-trivial upper bounds for general bilinear forms with trace functions of bountiful sheaves, where the supports of two variables can be...
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Pairs of square-free values of the type n2 + 1, n2 + 2
We show that there exist infinitely many consecutive square-free numbers of the form n 2 + 1, n 2 + 2. We also establish an asymptotic formula for the...
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On the Hybrid Power Mean Involving the Two-Term Exponential Sums and Polynomial Character Sums
The main purpose of this paper is using the analytic method and the properties of trigonometric sums and character sums to study the computational...
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Kloosterman Sums and a Problem of D. H. Lehmer
A classical problem of D. H. Lehmer suggests the study of distributions of elements of Z / p Z of opposite parity to the multiplicative inverse mod p ....
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The Fourth Power Mean of the General 3-dimensional Kloostermann Sums mod p
The main purpose of this paper is using the analytic methods, the solutions of the congruence equation mod p and the properties of Gauss sums to...
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Exponential sums involving automorphic forms for GL(3) over arithmetic progressions
Let f be a Hecke-Maass cusp form for SL(3,ℤ) with Fourier coeffcients A f ( m , n ), and let ϕ ( x ) be a C ∞ -function supported on [1, 2] with derivatives...
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On the fourth power mean of the generalized quadratic Gauss sums
The main purpose of this paper is to use elementary methods and properties of the classical Gauss sums to study the computational problem of one kind...
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A new hybrid power mean involving the generalized quadratic Gauss sums and sums analogous to Kloosterman sums *
The main purpose of this paper is using the analytic method and properties of the classical quadratic Gauss sums to study the computational problem...
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On critical values of twisted Artin L-functions
We give a simple proof that critical values of any Artin L -function attached to a representation ϱ with character χ ϱ are stable under twisting by a...
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The fourth power mean of the general 2-dimensional Kloostermann sums mod p
The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth...