52 citations · 127 across the 37 of their papers we have counts for
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math.CO2017
Variations on the sum-product problem II
Brendan Murphy, Oliver Roche-Newton, Ilya Shkredov
This is a sequel to the paper arXiv:1312.6438 by the same authors. In this sequel, we quantitatively improve several of the main results of arXiv:1312.6438, and build on the method…
math.NT2017
Analogues of the Balog--Wooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions
Oliver Roche-Newton, Igor Shparlinski, Arne Winterhof
Balog and Wooley have recently proved that any subset of either real numbers or of a prime finite field can be decomposed into two parts and , one of small additive ener…
math.CO2017★ 52 cited
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…