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Licensed Unlicensed Requires Authentication Published by De Gruyter April 30, 2013

Product graphs, sum-product graphs and sum-product estimates over finite rings

  • Le Anh Vinh EMAIL logo
From the journal Forum Mathematicum
https://doi.org/10.1515/forum-2012-0177

Abstract

In this paper, we study the product and sum-product graphs defined over the residue ring mod m. We show that all (or almost all) systems of dot-product equations are solvable in any sufficiently large subset ℰ ⊂ ℤmd. We also prove some results on sum-product estimates in ℤm.

Keywords: Bilinear equations; product graphs; sum-product graphs; sum-product estimates
MSC: 15A15

Funding source: Vietnam National Foundation for Science and Technology Development

Award Identifier / Grant number: 101.01-2011.28

Received: 2012-12-12
Revised: 2013-2-25
Published Online: 2013-4-30
Published in Print: 2015-5-1

© 2015 by De Gruyter

From the journal
Forum Mathematicum
Forum Mathematicum
Volume 27 Issue 3
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Frontmatter
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Upper triangular matrices and operations in odd primary connective K-theory
Solving quintic equations by two-fold origami
Orthogonality of polynomials and orthosymmetry
The moduli space of 4-dimensional non-nilpotent complex associative algebras
Improvement of eigenfunction estimates on manifolds of nonpositive curvature
Unramified representations of the universal central extension of SL2(𝔽q((z)))
Languages associated with saturated formations of groups
On some new model category structures from old, on the same underlying category
On functions of bounded Λ-variation and integral smoothness
Ring coproducts embedded in power-series rings
A uniform bound for geodesic periods of eigenfunctions on hyperbolic surfaces
Action-induced nested classes of groups and jump (co)homology
The convergence of the product γ˜p-1h0bn-1 in the Adams spectral sequence
Product graphs, sum-product graphs and sum-product estimates over finite rings
BV functions in a Gelfand triple for differentiable measure and its applications
The variety of nilpotent elements and invariant polynomial functions on the special algebra Sn
The Lefschetz coincidence class of p maps
The natural pseudo-distance as a quotient pseudo-metric, and applications
On a class of parametric Neumann problems with indefinite and unbounded potential
An estimate on the heat kernel of Schrödinger operators with non-negative potentials on nilpotent Lie groups and its applications
A hybrid Euler–Hadamard product and moments of ζ'(ρ)
Legendrian realization in convex Lefschetz fibrations and convex stabilizations
Recollements induced from tilting modules over tame hereditary algebras
Corrigendum to On some multiplicity and mixed multiplicity formulas [Forum Math. 26 (2014), 413–442]
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