TY - JOUR
T1 - An improved sum-product bound for quaternions
AU - Basit, Abdul
AU - Lund, Ben
N1 - Funding Information:
∗Received by the editors December 10, 2018; accepted for publication (in revised form) April 30, 2019; published electronically June 25, 2019. http://www.siam.org/journals/sidma/33-2/M123146.html Funding: Work on this project by the second author was supported by NSF grant DMS-1344994 (RTG in Algebra, Algebraic Geometry, and Number Theory, at the University of Georgia). †Department of Mathematics, 255 Hurley Hall, University of Notre Dame, Notre Dame, IN 46556 ([email protected]). ‡Department of Mathematics, Fine Hall, Princeton University, Princeton NJ 08544 ([email protected]).
Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics Publications. All rights reserved.
PY - 2019/6/25
Y1 - 2019/6/25
N2 - We show that there exists an absolute constant c ≥ 0, such that, for any finite set A of quaternions, max{|A + A|,|AA|} ≥|A|4/3+c. This generalizes a sum-product bound for real numbers proved by Konyagin and Shkredov.
AB - We show that there exists an absolute constant c ≥ 0, such that, for any finite set A of quaternions, max{|A + A|,|AA|} ≥|A|4/3+c. This generalizes a sum-product bound for real numbers proved by Konyagin and Shkredov.
KW - Additive combinatorics
KW - Quaternions
KW - Sum-product conjecture
UR - http://www.scopus.com/inward/record.url?scp=85069842624&partnerID=8YFLogxK
U2 - 10.1137/18M1231468
DO - 10.1137/18M1231468
M3 - Article
AN - SCOPUS:85069842624
SN - 0895-4801
VL - 33
SP - 1044
EP - 1060
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
IS - 2
ER -