Dr. Oliver Roche-Newton

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Oliver Roche-Newton

Peer Reviewed Journal Publication
  • Petridis, G.; Roche-Newton, O.; Rudnev, M.; Warren, A. (2020) An energy bound in the affine group. International Mathematics Research Notices, Bd. to appear, S. 10.
  • O. Roche-Newton, A. Warren (2020) New expander bounds from affine group energy. Discrete & Computational Geometry, Bd. to appear, S. 10.
  • Makhul, M.; Roche-Newton, O.; Warren, A.; Zeeuw, F. de (2020) Constructions for the Elekes-Szabó and Elekes-Rónyai problems. Electronic Journal of Combinatorics, Bd. to appear, S. 1--10.
  • Shkredov, O. Roche-Newton and Ilya D. (2019) If A+A is small then AAA is superquadratic. Journal of Number Theory, Bd. 201, S. 124-134.
  • Oliver Roche-Newton, Imre Z. Ruzsa, Chun-Yen Shen, Ilya D. Shkredov (2019) On the size of the set AA+A. Journal of the London Mathematical Society, Bd. 99 (2), S. 477-494.
  • O. Roche-Newton, I.E. Shparlinski, A. Winterhof (2019) Analogues of the Balog--Wooley decomposition for subsets of finite fields and character sums with convolutions. Annals of Combinatorics, Bd. 23 (1), S. 183-205.
  • O. Roche-Newton, A. Warren (2019) Improved bounds for pencils of lines. Proceedings of the American Mathematical Society, Bd. to appear, S. 10.
  • Brendan Murphy, Giorgis Petridis, Oliver Roche-Newton, Misha Rudnev, Ilya D. Shkredov (2019) New results on sum-product type growth over fields. Mathematika, Bd. 65 (3), S. 588-642.
  • Iosevich, A.; Roche-Newton, O.; Rudnev, M. (2018) On discrete values of bilinear forms. Mat. Sb, Bd. 209 (10), S. 71--88.
  • O. Roche-Newton, I. Shkredov, A. Winterhof (2018) Packing sets over finite abelian groups. Integers, Bd. 18 (Paper No. A38), S. 9 pp.
  • B. Hanson, B. Lund, O. Roche-Newton (2015) On distinct perpendicular bisectors and pinned distances in finite fields. Finite fields and their applications, Bd. 37, S. 240-264 (to appear 2016).
  • B. Murphy, O. Roche-Newton, I. Shkredov (2015) Variations on the sum-product problem. SIAM Journal on Discrete Mathematics, Bd. 29 (1), S. 514-540.
  • M. Rudnev, I. Shkredov, O. Roche-Newton (2015) New sum-product type estimates over finite fields. Advances in Mathematics, Bd. submitted, S. 10.
  • O. Raz, O. Roche-Newton, M. Sharir (2015) Sets with few distinct distances do not have heavy lines. Discrete Math., Bd. 338 (8), S. 1484-1492.
  • J. Cilleruelo, A. Iosevich, B. Lund, O. Roche-Newton, M. Rudnev (2015) Elementary methods for incidence problems in finite fields. Mathematische Zeitschrift, Bd. submitted, S. 10.
  • O. Roche-Newton, I. Shparlinski (2015) Polynomial values in subfields and affine subspaces of finite fields. Quarterly Journal of Mathematics, Bd. 66, S. 693-706.
  • A. Balog, O. Roche-Newton (2015, online: 2015) New sum-product estimates for real and complex number. Discrete and Computational Geometry, Bd. 53 (4), S. 825-846.
  • O. Roche-Newton, D. Zhelezov (2014, online: 2014) A bound on the multiplicative energy of a sum set and extremal sum-product problems. SMoscow Journal of Combinatorics and Number Theory, Bd. to appear, S. 10.
  • B. Hanson, O. Roche-Newton and D. Zhelezov (online: 2019) On iterated product sets with shifts. Mathematika, Bd. 65 (4), S. 831-850.

Conference Contribution: Publication in Proceedings
  • Roche-Newton, Oliver (2018) An improved bound for the size of the set A/A+A. (Symposium on Computational Geometry 2018); Budapest.
  • Roche-Newton, O. (2015, online: 2015) A short proof of a near-optimal cardinality estimate for the size of a product of a sum set., Proceedings of Symposium on Computational Geometry 2015, S. to appear.

Workingpaper
  • Roche-Newton, O.; Warren, A. (2020) Counting $k$-arcs in $F_{q^2}$O. Roche-Newton A. Warren.