EXPONENTIAL SUMS WITH THE BINOMIAL IN THE EXPONENT OVER THE RING OF GAUSSIAN INTEGERS
Journal Title: Дослідження в математиці і механіці - Year 2014, Vol 19, Issue 3
Abstract
In this work nontrivial estimates for the exponential sums with the polynomial ..(..) = ...... + .... in the exponent, where (.., ..) = (.., ..) = (.., ..) = 1, .. > 2, over the ring of the gaussian integers were obtained.
Authors and Affiliations
L. V. Balyas
Averaging of differential equations of movement for the ship on the direct course
The possibility of applying the full averaging scheme to the ship complex control problem is considered in the article. The model of this problem was first described by V. I. Nebesnov and V. A. Plotnikov and F. Y. Kuzyu...
ASYMPTOTIC REPRESENTATIONS OF SOLUTIONS WITH SLOWLY VARYING DERIVATIVES
Second-order differential equations with power and exponential nonlinearities on the right hand side play an important role in the development of a qualitative theory of differential equations. The authors of most works...
Variational method of homogeneous solutions for axisymmetric elasticity problems
A variational method of homogeneous solutions for solving of axisymmetric elasticity problems for semiinfinite and finite cylinders with free lateral surface has been developed. As an example of application of the method...
ON THE MULTIPLICATIVE PARTITION FUNCTION
We study the number of representations n=s1⋯sm, where sj are sonor numbers, i.e. for every sj there do not exist the natural numbers n and k such that sj=nk, k⩾2. The counting function f(n) of such representation is the...
AN ITERATIVE ALGORITHM FOR CALCULATION OF EIGENVALUES AND EIGENFUNCTIONS OF THE STURM--LIOUVILLE PROBLEM
An iterative algorithm for computing the i-th eigenvalue (e. v.) and the corresponding eigenfunction (e. f.) of the Sturm--Liouville problem on a finite interval is proposed. The algorithm uses the well-known asymptotic...