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- Alex Iosevich, Michael Rudnev, Yujia Zhai
- Combinatorica
- 2015

Abstract. In this paper, we will show that if E is a subset of a planar point set over a finite field Fq (q not necessarily prime) and has cardinality |E| > 64q log2 q, then there are more than q 2â€¦ (More)

- Sergei Konyagin, Michael Rudnev
- SIAM J. Discrete Math.
- 2013

Abstract. New lower bounds involving sum, difference, product, and ratio sets of a set A âŠ‚ C are given. The estimates involving the sum set match, up to constants, the state-of-the-art estimates,â€¦ (More)

- Alex Iosevich, Michael Rudnev
- Discrete & Computational Geometry
- 2007

In this paper we investigate the ErdÃ¶s/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper boundâ€¦ (More)

- Alex Iosevich, Sergei Konyagin, Michael Rudnev, V. Ten
- Discrete & Computational Geometry
- 2006

We show that the equation si1 + si2 + Â· Â· Â·+ sid = sid+1 + Â· Â· Â·+ si2d has O N2dâˆ’2+2 âˆ’d+1 solutions for any strictly convex sequence {si}i=1 without any additional arithmetic assumptions. The proofâ€¦ (More)

- Michael Rudnev
- Combinatorica
- 2018

- Michael Rudnev, V. Ten
- 2005

We propose a model for local dynamics of a perturbed convex real-analytic Liouville-integrable Hamiltonian system near a resonance of multiplicity 1 + m, m â‰¥ 0. Physically, the model represents aâ€¦ (More)

- Michael Rudnev, V. Ten
- 2004

We establish a generic sufficient condition for a compact n-dimensional manifold bearing an integrable geodesic flow to be the n-torus. As a complementary result, we show that in the case of domainsâ€¦ (More)

We consider a near-integrable Hamiltonian system in action-angle variables with analytic Hamiltonian. For a given resonant surface of multi-plicity one we show that near a Cantor set of points onâ€¦ (More)

- A. A. YUROVA, Artyom V. Yurov, Michael Rudnev
- 2002

We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two by developing a Darboux (Moutard) transformation formalism for this problem. Theâ€¦ (More)

- Vsevolod F. Lev, Michael Rudnev
- Discrete & Computational Geometry
- 2018

Consider the projections of a finite set A âŠ‚ Rn onto the coordinate hyperplanes; how small can the sum of the sizes of these projections be, given the size of A? In a different form, this problem hasâ€¦ (More)