On a girth–free variant of the Bourgain–Gamburd machine

Finite Fields and Their Applications - Tập 90 - Trang 102225 - 2023
I.D. Shkredov1,2
1Steklov Mathematical Institute, ul. Gubkina, 8, Moscow, 119991, Russia
2London Institute for Mathematical Sciences, Royal Institution, 21 Albermarle St, London W1S 4BS, UK

Tài liệu tham khảo

Bourgain, 2008, Uniform expansion bounds for Cayley graphs of SL2(Fp), Ann. Math., 167, 625, 10.4007/annals.2008.167.625

Bourgain, 2012, On the hidden shifted power problem, SIAM J. Comput., 41, 1524, 10.1137/110850414

de la Bretèche, 2021, Small Gál sums and applications, J. Lond. Math. Soc., 103, 336, 10.1112/jlms.12378

Burgess, 1962, On character sums and primitive roots, Proc. Lond. Math. Soc. (3), 12, 179, 10.1112/plms/s3-12.1.179

Burgess, 1963, A note on the distribution of residues and non–residues, J. Lond. Math. Soc., 1, 253, 10.1112/jlms/s1-38.1.253

Cilleruelo, 2011, Concentration of points on two and three dimensional modular hyperbolas and applications, Geom. Funct. Anal., 21, 892, 10.1007/s00039-011-0127-6

Dinai, 2011, Growth in SL2 over finite fields, J. Group Theory, 14, 273, 10.1515/jgt.2010.056

He

He

Helfgott, 2008, Growth and generation in SL2(Z/pZ), Ann. Math., 167, 601, 10.4007/annals.2008.167.601

Iwaniec, 2004

Kerr, 2020, A refinement of the Burgess bound for character sums, Mich. Math. J., 69, 227, 10.1307/mmj/1573700737

Magnus, 2004, Presentations of Groups in Terms of Generators and Relations

N.G. Moshchevitin, B. Murphy, I.D. Shkredov, on Korobov's bound concerning Zaremba's conjecture, preprint.

Pólya, 1918, 21

Rudnev

Shkredov, 2021, Noncommutative methods in Additive Combinatorics and Number Theory, Russ. Math. Surv., 76, 1065, 10.1070/RM10029

Shkredov

Shkredov

Suzuki, 1982

Tao, 2006

Warren

Vinogradov, 1918, Sur la distribution des résidus et des non–résidus des puissances, J. Phys.–Math. Soc. Perm., 1, 94

Vinogradov, 1985