7 papers
On polynomial expanders with many variables
M. Z. Garaev, S. V. Konyagin
For a fixed integer we consider the homogeneous polynomial We prove that, for any fin…
Upper and lower estimates for integer complexity
Sergei Konyagin, Kristina Oganesyan
Let stand for the integer complexity of the number , i.e. for the least number of 's needed to write using arbitrary many additions, multiplications, and parenthe…
On Sidon sets with squares, cubes and quartics in short intervals
M. Z. Garaev, F. M. Garayev, S. V. Konyagin
Representative examples of our results are as follows. For any positive integer the equation has n…
Unique expansions in number systems via refinement equations
Sergei V. Konyagin, Vladimir Yu. Protasov, Alexey L. Talambutsa
Using the subdivision schemes theory, we develop a criterion to check if any natural number has at most one representation in the -ary number system with a set of non-negative i…
On Distinct Angles in the Plane
Sergei V. Konyagin, Jonathan Passant, Misha Rudnev
We prove that if points lie in convex position in the plane then they determine distinct angles, provided that the points do not lie on a common circle. This is de…
Trigonometric polynomials with frequencies in the set of cubes
Mikhail R. Gabdullin, Sergei V. Konyagin
We prove that for any and any trigonometric polynomial with frequencies in the set , one has with imp…
New sum product type estimates
Sergei V. Konyagin, Misha Rudnev
New lower bounds involving sum, difference, product, and ratio sets for a set $A\subset \C$ are given. The estimates involving the sum set match, up to constants, the one obtained…