52 citations · 208 across the 22 of their papers we have counts for
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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…
Upper Bounds on the Cardinality of Higher Sumsets
Giorgis Petridis
Let A and B be finite sets in a commutative group. We bound |A+hB| in terms of |A|, |A+B| and h. We provide a submultiplicative upper bound that improves on the existing bound of I…
New Proofs of Plünnecke-type Estimates for Product Sets in Groups
Giorgis Petridis
We present a new method to bound the cardinality of triple product sets in groups and give three applications. A new and unexpectedly short proof of the Plunnecke-Ruzsa sumset ineq…
Plünnecke's Inequality
Giorgis Petridis
Plunnecke's inequality is the standard tool to obtain estimates on the cardinality of sumsets and has many applications in additive combinatorics. We present a new proof. The main…