Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E. Character sums and deterministic polynomial root finding in finite fields. (English) Zbl 1400.11153 Math. Comput. 84, No. 296, 2969-2977 (2015). MSC: 11T06 11Y16 11T23 68Q25 PDFBibTeX XMLCite \textit{J. Bourgain} et al., Math. Comput. 84, No. 296, 2969--2977 (2015; Zbl 1400.11153) Full Text: DOI arXiv
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. Multiplicative congruences with variables from short intervals. (English) Zbl 1385.11002 J. Anal. Math. 124, 117-147 (2014). MSC: 11A07 11L05 PDFBibTeX XMLCite \textit{J. Bourgain} et al., J. Anal. Math. 124, 117--147 (2014; Zbl 1385.11002) Full Text: DOI arXiv
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. On congruences with products of variables from short intervals and applications. (English) Zbl 1301.11041 Proc. Steklov Inst. Math. 280, 61-90 (2013); reprinted from Tr. Mat. Inst. Steklova 280, 67-96 (2013). Reviewer: Enzo Bonacci (Latina) MSC: 11D79 11L40 11A07 11T24 PDFBibTeX XMLCite \textit{J. Bourgain} et al., Proc. Steklov Inst. Math. 280, 61--90 (2013; Zbl 1301.11041) Full Text: DOI arXiv
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. On the hidden shifted power problem. (English) Zbl 1311.11111 SIAM J. Comput. 41, No. 6, 1524-1557 (2012). MSC: 11T06 11Y16 68Q25 94A60 PDFBibTeX XMLCite \textit{J. Bourgain} et al., SIAM J. Comput. 41, No. 6, 1524--1557 (2012; Zbl 1311.11111) Full Text: DOI arXiv
Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E. Distribution of elements of cosets of small subgroups and applications. (English) Zbl 1290.11017 Int. Math. Res. Not. 2012, No. 9, 1968-2009 (2012). Reviewer: Ilya D. Shkredov (Moskva) MSC: 11B30 PDFBibTeX XMLCite \textit{J. Bourgain} et al., Int. Math. Res. Not. 2012, No. 9, 1968--2009 (2012; Zbl 1290.11017) Full Text: DOI arXiv
Bourgain, Jean; Dilworth, Stephen J.; Ford, Kevin; Konyagin, Sergei V.; Kutzarova, Denka Breaking the \(k^2\) barrier for explicit RIP matrices. (English) Zbl 1288.68062 Proceedings of the 43rd annual ACM symposium on theory of computing, STOC ’11. San Jose, CA, USA, June 6–8, 2011. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0691-1). 637-644 (2011). MSC: 68P30 68W05 PDFBibTeX XMLCite \textit{J. Bourgain} et al., in: Proceedings of the 43rd annual ACM symposium on theory of computing, STOC '11. San Jose, CA, USA, June 6--8, 2011. New York, NY: Association for Computing Machinery (ACM). 637--644 (2011; Zbl 1288.68062) Full Text: DOI
Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka Explicit constructions of RIP matrices and related problems. (English) Zbl 1236.94027 Duke Math. J. 159, No. 1, 145-185 (2011). MSC: 94A12 11T23 11B13 11B30 41A46 94B60 PDFBibTeX XMLCite \textit{J. Bourgain} et al., Duke Math. J. 159, No. 1, 145--185 (2011; Zbl 1236.94027) Full Text: DOI arXiv Backlinks: MO
Bourgain, Jean; Konyagin, Sergei; Shparlinski, Igor Distribution on elements of cosets of small subgroups and applications. arXiv:1103.0567 Preprint, arXiv:1103.0567 [math.NT] (2011). MSC: 11A15 11L07 11N25 BibTeX Cite \textit{J. Bourgain} et al., ``Distribution on elements of cosets of small subgroups and applications'', Preprint, arXiv:1103.0567 [math.NT] (2011) Full Text: arXiv OA License
Bourgain, Jean; Ford, Kevin; Konyagin, Sergei V.; Shparlinski, Igor E. On the divisibility of Fermat quotients. (English) Zbl 1223.11116 Mich. Math. J. 59, No. 2, 313-328 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11N69 11A07 11N36 11L07 PDFBibTeX XMLCite \textit{J. Bourgain} et al., Mich. Math. J. 59, No. 2, 313--328 (2010; Zbl 1223.11116) Full Text: DOI
Bourgain, Jean; Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E. On the smallest pseudopower. (English) Zbl 1242.11006 Acta Arith. 140, No. 1, 43-55 (2009). Reviewer: Florian Luca (Morelia) MSC: 11A07 11L07 PDFBibTeX XMLCite \textit{J. Bourgain} et al., Acta Arith. 140, No. 1, 43--55 (2009; Zbl 1242.11006) Full Text: DOI
Bombieri, E.; Bourgain, J.; Konyagin, S. V. Roots of polynomials in subgroups of \(\mathbb F_p^{\ast}\) and applications to congruences. (English) Zbl 1213.11058 Int. Math. Res. Not. 2009, No. 5, 802-834 (2009). MSC: 11C08 11G25 11T06 12E10 13M10 14G15 PDFBibTeX XMLCite \textit{E. Bombieri} et al., Int. Math. Res. Not. 2009, No. 5, 802--834 (2009; Zbl 1213.11058) Full Text: DOI
Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E. Product sets of rationals, multiplicative translates of subgroups in residue rings, and fixed points of the discrete logarithm. (English) Zbl 1232.11003 Int. Math. Res. Not. 2008, Article ID rnn090, 29 p. (2008); corrigenda 2009, No. 16, 3146-3147 (2009). MSC: 11A07 11B57 PDFBibTeX XMLCite \textit{J. Bourgain} et al., Int. Math. Res. Not. 2008, Article ID rnn090, 29 p. (2008; Zbl 1232.11003) Full Text: DOI
Bourgain, J.; Glibichuk, A. A.; Konyagin, S. V. Estimates for the number of sums and products and for exponential sums in fields of prime order. (English) Zbl 1093.11057 J. Lond. Math. Soc., II. Ser. 73, No. 2, 380-398 (2006). Reviewer: Angel V. Kumchev (Towson) MSC: 11B30 11L07 11L05 11T23 PDFBibTeX XMLCite \textit{J. Bourgain} et al., J. Lond. Math. Soc., II. Ser. 73, No. 2, 380--398 (2006; Zbl 1093.11057) Full Text: DOI
Bourgain, Jean; Konyagin, S. V. Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order. (English. Abridged French version) Zbl 1041.11056 C. R., Math., Acad. Sci. Paris 337, No. 2, 75-80 (2003). Reviewer: John H. Loxton (North Ryde) MSC: 11L07 11T23 PDFBibTeX XMLCite \textit{J. Bourgain} and \textit{S. V. Konyagin}, C. R., Math., Acad. Sci. Paris 337, No. 2, 75--80 (2003; Zbl 1041.11056) Full Text: DOI