On exponential sums involving the divisor function over Z[๐]
Journal Title: ะะพัะปัะดะถะตะฝะฝั ะฒ ะผะฐัะตะผะฐัะธัั ั ะผะตั ะฐะฝััั - Year 2016, Vol 21, Issue 2
Abstract
We apply the van der Corput transform to investigate the sums of view ฮฃ๏ธ ๐(๐)๐(๐)๐(๐(๐))), where ๐(๐) is the number of representations of ๐ as the sum of two squares of integer numbers. Such sums have been studied by M. Jutila, O. Gunyavy, M. Huxley and etc. Depending of differential properties of the functions ๐(๐) and ๐(๐) there have been obtained the different kinds of error terms in bounds of the considered sums. In the special case, O. Gunyavy improved the result of M. Jutila in the problem on estimate the exponential sum involving the divisor function ๐ (๐). We obtain the asymptotic formula of the sum ฮฃ๏ธ ๐ (๐ผ)๐ (๏ธ ๐ ๐๐(๐ผ) )๏ธ over the ring of Gaussian integers which is an analogue of the asymptotic formulas obtained by M. Jutila and O. Gunyavy. MSC: 11K45.
Authors and Affiliations
S. Varbanets
Keywords
Related Articles
- EP ID EP191239
- DOI -
- Views 55
- Downloads 0
Split of gas stream onto the bubbles inside liquid
A theory of the approximate description of the splitting of the thin jat of ideal gas flowing into the incompressible frictionless liquid is constructed on the base of the balance equations of mass and energy. Under the...
HIGH-ORDER CLUSTER INTEGRALS FOR THE LATTICE-GAS MODEL
In the paper, for the known statistical lattice-gas model, a new method is proposed to define the high-order reducible cluster integrals on the basis of the Cauchy--Hadamard theorem and recently established strict inform...
STABILITY OF UNIFORM ATTRACTORS FOR ONE CLASS OF IMPULSIVE PARABOLIC SYSTEMS
In this paper we consider weakly non-linear two-dimensional parabolic systems, whose solutions have jumps at moments of intersection with fixed (impulsive) subset of the phase space. It generates impulsive dynamical syst...
ASYMPTOTICS OF SLOWLY VARYING SOLUTIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS WITH REGULARLY AND RAPIDLY VARYING NONLINEARITIES.
In this paper for the second-order differential equation which has a right-hand side containing the sum of the terms with regularly and rapidly varying nonlinearities the necessary and sufficient conditions of the existe...
Some remarks on the absolute continuity of set-valued mappings
Recently, many authors have considered the existence, uniqueness and properties of solutions of set-valued differential and integral-differential equations, higher-order equations and investigated impulsive and control s...