52 citations · 208 across the 22 of their papers we have counts for
27 papers
Refined upper bounds on Schur-like numbers
Swaroop Hegde, Andrew Lott, Giorgis Petridis +1
For positive integers and , every -coloring of contains a monochromatic solution to provided that $N \ge 3^r (r!)^{…
More on the sum-product problem for integers with few prime factors
Rishika Agrawal, Thomas F. Bloom, Giorgis Petridis
We show that if is a finite set of integers in which every integer is divisible by many primes then \[\max(\lvert A+A\rvert,\lvert AA\rvert) \geq \lver…
Polynomial configurations in dense subsets of the prime lattice
Andrew Lott, Ákos Magyar, Giorgis Petridis +1
We provide a multidimensional extension of previous results on the existence of polynomial progressions in dense subsets of the primes. Let be a subset of the prime lattice - t…
Almost orthogonal subsets of vector spaces over finite fields
Ali Mohammadi, Giorgis Petridis
We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In parti…
A question of Bukh on sums of dilates
Brandon Hanson, Giorgis Petridis
We answer in the affirmative a question of Bukh on the cardinality of the dilate sum .
Bounds of Trilinear and Trinomial Exponential Sums
Simon Macourt, Giorgis Petridis, Ilya D. Shkredov +1
We prove, for a sufficiently small subset of a prime residue field, an estimate on the number of solutions to the equation w…
On the Pinned Distances Problem in Positive Characteristic
Brendan Murphy, Giorgis Petridis, Thang Pham +2
We study the Erd\H os-Falconer distance problem for a set , where is a field of positive characteristic . If and th…
An Energy Bound in the Affine Group
Giorgis Petridis, Oliver Roche-Newton, Misha Rudnev +1
We prove a nontrivial energy bound for a finite set of affine transformations over a general field and discuss a number of implications. These include new bounds on growth in the a…
An example related to the Erdos-Falconer question over arbitrary finite fields
Brendan Murphy, Giorgis Petridis
There exists an infinite family of examples of subsets of with elements whose distance sets are not the whole of .
Refined Estimates Concerning Sumsets Contained in the Roots of Unity
Brandon Hanson, Giorgis Petridis
We prove that the clique number of the Paley graph is at most , and that any supposed additive decompositions of the set of quadratic residues can only come from co…
Bisectors and pinned distances
Ben Lund, Giorgis Petridis
We prove, under suitable conditions, a lower bound on the number of pinned distances determined by small subsets of two-dimensional vector spaces over fields. For finite subsets of…
Products of Differences over Arbitrary Finite Fields
Brendan Murphy, Giorgis Petridis
There exists an absolute constant such that for all and all subsets of the finite field with elements, if , then \[ |(A…
New results on sum-product type growth over fields
Brendan Murphy, Giorgis Petridis, Oliver Roche-Newton +2
We prove a range of new sum-product type growth estimates over a general field , in particular the special case . They are unified by the theme…
A Second Wave of Expanders over Finite Fields
Brendan Murphy, Giorgis Petridis
This is an expository survey on recent sum-product results in finite fields. We present a number of sum-product or "expander" results that say that if then some set…
Collinear triples and quadruples for Cartesian products in
Giorgis Petridis
In this ote, which has been absorbed by arXiv1702.01003, we combine a recent point-line incidence bound of Stevens and de Zeeuw with an older lemma of Bourgain, Katz and Tao to bou…
Pinned algebraic distances determined by Cartesian products in
Giorgis Petridis
Let be an odd prime and be a subset of the finite field with elements. We show that determines at least a c…
Bounds on trilinear and quadrilinear exponential sums
Giorgis Petridis, Igor E. Shparlinski
We use an estimate of Aksoy Yazici, Murphy, Rudnev and Shkredov (2016) on the number of solutions of certain equations involving products and differences of sets in prime finite fi…
A point-line incidence identity in finite fields, and applications
Brendan Murphy, Giorgis Petridis
Let be a set in the 2-dimensional vector space over a finite field with elements. We prove an identity for the second moment of its incidence funct…
Products of Differences in Prime Order Finite Fields
Giorgis Petridis
There exists an absolute constant with the following property. Let be a set in the prime order finite field with elements. Suppose that $|A| > C…
On the Number of Dot Products Determined by a Large Set and One of its Translates in Finite Fields
Giorgis Petridis
Let be a set in the 2-dimensional vector space over a finite field with elements, which satisfies . There exist such that $|E…
Tiling sets and spectral sets over finite fields
C. Aten, B. Ayachi, E. Bau +14
We study tiling and spectral sets in vector spaces over prime fields. The classical Fuglede conjecture in locally compact abelian groups says that a set is spectral if and only if…
The Cardinality of Sumsets: Different Summands
Brendan Murphy, Eyvindur Ari Palsson, Giorgis Petridis
Let be a positive integer and be finite sets in a commutative group. We bound from above in terms of and…
Matchings in Random Biregular Bipartite Graphs
Guillem Perarnau, Giorgis Petridis
We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdos and…
The L^1-norm of exponential sums in Z^d
Giorgis Petridis
Let A be a finite set of integers and F_A its exponential sum. McGehee, Pigno & Smith and Konyagin have independently proved that the L^1-norm of F_A is at least c log|A| for some…