Bilyk, Dmitriy; Mastrianni, Michelle Lower bounds for the directional discrepancy with respect to an interval of rotations. (English) Zbl 1523.11139 J. Fourier Anal. Appl. 29, No. 3, Paper No. 25, 16 p. (2023). Reviewer: Anton Shutov (Vladimir) MSC: 11K38 42B05 52A10 PDFBibTeX XMLCite \textit{D. Bilyk} and \textit{M. Mastrianni}, J. Fourier Anal. Appl. 29, No. 3, Paper No. 25, 16 p. (2023; Zbl 1523.11139) Full Text: DOI arXiv
Bilyk, Dmitriy; Matzke, Ryan W.; Vlasiuk, Oleksandr Positive definiteness and the Stolarsky invariance principle. (English) Zbl 1505.11103 J. Math. Anal. Appl. 513, No. 2, Article ID 126220, 30 p. (2022). Reviewer: Peter Kritzer (Linz) MSC: 11K38 31B15 46N10 PDFBibTeX XMLCite \textit{D. Bilyk} et al., J. Math. Anal. Appl. 513, No. 2, Article ID 126220, 30 p. (2022; Zbl 1505.11103) Full Text: DOI arXiv
Bilyk, Dmitriy On some recent developments in uniform distribution and discrepancy theory. (English) Zbl 1459.11160 Bilyk, Dmitriy (ed.) et al., Discrepancy theory. Berlin: De Gruyter. Radon Ser. Comput. Appl. Math. 26, 1-20 (2020). MSC: 11K38 PDFBibTeX XMLCite \textit{D. Bilyk}, Radon Ser. Comput. Appl. Math. 26, 1--20 (2020; Zbl 1459.11160) Full Text: DOI
Bilyk, Dmitriy; Dai, Feng Geodesic distance Riesz energy on the sphere. (English) Zbl 1470.11208 Trans. Am. Math. Soc. 372, No. 5, 3141-3166 (2019). MSC: 11K38 74G65 42C10 33C55 PDFBibTeX XMLCite \textit{D. Bilyk} and \textit{F. Dai}, Trans. Am. Math. Soc. 372, No. 5, 3141--3166 (2019; Zbl 1470.11208) Full Text: DOI arXiv
Bilyk, Dmitriy; Dai, Feng; Steinerberger, Stefan General and refined Montgomery lemmata. (English) Zbl 1419.42005 Math. Ann. 373, No. 3-4, 1283-1297 (2019). MSC: 42B05 11K38 35B05 35B40 52C35 PDFBibTeX XMLCite \textit{D. Bilyk} et al., Math. Ann. 373, No. 3--4, 1283--1297 (2019; Zbl 1419.42005) Full Text: DOI arXiv
Bilyk, Dmitriy; Matzke, Ryan W. On the Fejes Tóth problem about the sum of angles between lines. (English) Zbl 1458.11119 Proc. Am. Math. Soc. 147, No. 1, 51-59 (2019). MSC: 11K38 52C35 PDFBibTeX XMLCite \textit{D. Bilyk} and \textit{R. W. Matzke}, Proc. Am. Math. Soc. 147, No. 1, 51--59 (2019; Zbl 1458.11119) Full Text: DOI arXiv Backlinks: MO
Aistleitner, Christoph; Bilyk, Dmitriy; Nikolov, Aleksandar Tusnády’s problem, the transference principle, and non-uniform QMC sampling. (English) Zbl 1412.65002 Owen, Art B. (ed.) et al., Monte Carlo and quasi-Monte Carlo methods, MCQMC 2016. Proceedings of the 12th international conference on ‘Monte Carlo and quasi-Monte Carlo methods in scientific computing’, Stanford, CA, August 14–19, 2016. Cham: Springer. Springer Proc. Math. Stat. 241, 169-180 (2018). MSC: 65C05 60E15 PDFBibTeX XMLCite \textit{C. Aistleitner} et al., Springer Proc. Math. Stat. 241, 169--180 (2018; Zbl 1412.65002) Full Text: DOI arXiv
Bilyk, Dmitriy; Dai, Feng; Matzke, Ryan The Stolarsky principle and energy optimization on the sphere. (English) Zbl 1426.11075 Constr. Approx. 48, No. 1, 31-60 (2018). Reviewer: Volker Ziegler (Salzburg) MSC: 11K38 74G65 42A82 PDFBibTeX XMLCite \textit{D. Bilyk} et al., Constr. Approx. 48, No. 1, 31--60 (2018; Zbl 1426.11075) Full Text: DOI arXiv
Bilyk, Dmitriy; Markhasin, Lev BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension. (English) Zbl 1418.11112 J. Anal. Math. 135, No. 1, 249-269 (2018). MSC: 11K38 42B25 46E35 PDFBibTeX XMLCite \textit{D. Bilyk} and \textit{L. Markhasin}, J. Anal. Math. 135, No. 1, 249--269 (2018; Zbl 1418.11112) Full Text: DOI arXiv
Bilyk, Dmitry; Lacey, Michael T. One-bit sensing, discrepancy and Stolarsky’s principle. (English. Russian original) Zbl 1388.11052 Sb. Math. 208, No. 6, 744-763 (2017); translation from Mat. Sb. 208, No. 6, 4-25 (2017). Reviewer: Robert F. Tichy (Graz) MSC: 11K38 94A12 PDFBibTeX XMLCite \textit{D. Bilyk} and \textit{M. T. Lacey}, Sb. Math. 208, No. 6, 744--763 (2017; Zbl 1388.11052); translation from Mat. Sb. 208, No. 6, 4--25 (2017) Full Text: DOI arXiv
Bilyk, Dmitriy; Feldheim, Naomi The two-dimensional small ball inequality and binary nets. (English) Zbl 1376.42050 J. Fourier Anal. Appl. 23, No. 4, 817-833 (2017). Reviewer: Christoph Aistleitner (Graz) MSC: 42C40 11K38 PDFBibTeX XMLCite \textit{D. Bilyk} and \textit{N. Feldheim}, J. Fourier Anal. Appl. 23, No. 4, 817--833 (2017; Zbl 1376.42050) Full Text: DOI arXiv
Bilyk, Dmitriy; Ma, Xiaomin; Pipher, Jill; Spencer, Craig Diophantine approximations and directional discrepancy of rotated lattices. (English) Zbl 1334.11059 Trans. Am. Math. Soc. 368, No. 6, 3871-3897 (2016). Reviewer: Huaning Liu (Shaanxi) MSC: 11K38 11K60 28A78 52C05 PDFBibTeX XMLCite \textit{D. Bilyk} et al., Trans. Am. Math. Soc. 368, No. 6, 3871--3897 (2016; Zbl 1334.11059) Full Text: DOI Link
Bilyk, Dmitriy Roth’s orthogonal function method in discrepancy theory and some new connections. (English) Zbl 1358.11083 Chen, William (ed.) et al., A panorama of discrepancy theory. Cham: Springer (ISBN 978-3-319-04695-2/pbk; 978-3-319-04696-9/ebook). Lecture Notes in Mathematics 2107, 71-158 (2014). MSC: 11K38 11K06 11-02 PDFBibTeX XMLCite \textit{D. Bilyk}, Lect. Notes Math. 2107, 71--158 (2014; Zbl 1358.11083) Full Text: DOI
Amirkhanyan, Gagik; Bilyk, Dmitriy; Lacey, Michael T. Dichotomy results for the \(L^1\) norm of the discrepancy function. (English) Zbl 1370.11093 J. Math. Anal. Appl. 410, No. 1, 1-6 (2014). MSC: 11K38 PDFBibTeX XMLCite \textit{G. Amirkhanyan} et al., J. Math. Anal. Appl. 410, No. 1, 1--6 (2014; Zbl 1370.11093) Full Text: DOI arXiv
Bilyk, Dmitriy The \(L^{2}\) discrepancy of irrational lattices. (English) Zbl 1312.11062 Dick, Josef (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2012. Proceedings of the 10th international conference on ‘Monte Carlo and quasi-Monte Carlo methods in scientific computing’, Sydney, Australia, February 13–17, 2012. Berlin: Springer (ISBN 978-3-642-41094-9/hbk; 978-3-642-41095-6/ebook). Springer Proceedings in Mathematics & Statistics 65, 289-296 (2013). Reviewer: Yukio Ohkubo (Kagoshima) MSC: 11K38 PDFBibTeX XMLCite \textit{D. Bilyk}, Springer Proc. Math. Stat. 65, 289--296 (2013; Zbl 1312.11062) Full Text: DOI
Bilyk, Dmitriy; Lacey, Michael The supremum norm of the discrepancy function: recent results and connections. (English) Zbl 1304.11074 Dick, Josef (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2012. Proceedings of the 10th international conference on ‘Monte Carlo and quasi-Monte Carlo methods in scientific computing’, Sydney, Australia, February 13–17, 2012. Berlin: Springer (ISBN 978-3-642-41094-9/hbk; 978-3-642-41095-6/ebook). Springer Proceedings in Mathematics & Statistics 65, 23-38 (2013). Reviewer: Robert F. Tichy (Graz) MSC: 11K38 11K06 PDFBibTeX XMLCite \textit{D. Bilyk} and \textit{M. Lacey}, Springer Proc. Math. Stat. 65, 23--38 (2013; Zbl 1304.11074) Full Text: DOI arXiv
Bilyk, Dmitriy; Temlyakov, Vladimir N.; Yu, Rui The \(L_2\) discrepancy of two-dimensional lattices. (English) Zbl 1275.11111 Bilyk, Dmitriy (ed.) et al., Recent advances in harmonic analysis and applications. In honor of Konstantin Oskolkov on the occasion of his 65th birthday. Based on the AMS sectional meeting, Georgia Southern University, Statesboro, GA, USA, March 11–13, 2011. Berlin: Springer (ISBN 978-1-4614-4564-7/hbk; 978-1-4614-4565-4/ebook). Springer Proceedings in Mathematics & Statistics 25, 63-77 (2013). Reviewer: Roman Urban (Wrocław) MSC: 11K38 PDFBibTeX XMLCite \textit{D. Bilyk} et al., Springer Proc. Math. Stat. 25, 63--77 (2013; Zbl 1275.11111) Full Text: DOI
Bilyk, Dmitriy; Temlyakov, V. N.; Yu, Rui Fibonacci sets and symmetrization in discrepancy theory. (English) Zbl 1257.11074 J. Complexity 28, No. 1, 18-36 (2012). Reviewer: Roman Urban (Wrocław) MSC: 11K38 65C05 11B39 65D30 PDFBibTeX XMLCite \textit{D. Bilyk} et al., J. Complexity 28, No. 1, 18--36 (2012; Zbl 1257.11074) Full Text: DOI
Bilyk, Dmitriy On Roth’s orthogonal function method in discrepancy theory. (English) Zbl 1338.11073 Unif. Distrib. Theory 6, No. 1, 143-184 (2011). MSC: 11K38 11K06 PDFBibTeX XMLCite \textit{D. Bilyk}, Unif. Distrib. Theory 6, No. 1, 143--184 (2011; Zbl 1338.11073)
Bilyk, Dmitriy; Ma, Xiaomin; Pipher, Jill; Spencer, Craig Directional discrepancy in two dimensions. (English) Zbl 1250.11075 Bull. Lond. Math. Soc. 43, No. 6, 1151-1166 (2011). Reviewer: Robert F. Tichy (Graz) MSC: 11K38 11K06 PDFBibTeX XMLCite \textit{D. Bilyk} et al., Bull. Lond. Math. Soc. 43, No. 6, 1151--1166 (2011; Zbl 1250.11075) Full Text: DOI arXiv
Bilyk, Dmitriy; Lacey, Michael T.; Parissis, Ioannis; Vagharshakyan, Armen A three-dimensional signed small ball inequality. (English) Zbl 1223.11094 Berkes, István (ed.) et al., Dependence in probability, analysis and number theory. A volume in memory of Walter Philipp. Most papers based on the presentations at the conference, Graz, Austria, June 17–20, 2009. Heber City, UT: Kendrick Press (ISBN 0-9793183-8-6/pbk). 73-87 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11K38 PDFBibTeX XMLCite \textit{D. Bilyk} et al., in: Dependence in probability, analysis and number theory. A volume in memory of Walter Philipp. Most papers based on the presentations at the conference, Graz, Austria, June 17--20, 2009. Heber City, UT: Kendrick Press. 73--87 (2010; Zbl 1223.11094) Full Text: arXiv
Bilyk, Dmitriy; Lacey, Michael T.; Parissis, Ioannis; Vagharshakyan, Armen Exponential squared integrability of the discrepancy function in two dimensions. (English) Zbl 1198.42001 Mathematika 55, No. 1-2, 1-27 (2009). Reviewer: Kathryn Hare (Waterloo) MSC: 42B35 11K38 PDFBibTeX XMLCite \textit{D. Bilyk} et al., Mathematika 55, No. 1--2, 1--27 (2009; Zbl 1198.42001) Full Text: DOI arXiv
Bilyk, Dmitriy Cyclic shifts of the van der Corput set. (English) Zbl 1247.11099 Proc. Am. Math. Soc. 137, No. 8, 2591-2600 (2009). Reviewer: Christoph Aistleitner (Sydney) MSC: 11K38 42B05 PDFBibTeX XMLCite \textit{D. Bilyk}, Proc. Am. Math. Soc. 137, No. 8, 2591--2600 (2009; Zbl 1247.11099) Full Text: DOI arXiv
Bilyk, Dmitriy; Lacey, Michael; Vagharshakyan, Armen On the signed small ball inequality. (English) Zbl 1186.60009 Online J. Anal. Comb. 3, Article 6, 7 p. (2008). MSC: 60E15 11K38 41A46 42A55 PDFBibTeX XMLCite \textit{D. Bilyk} et al., Online J. Anal. Comb. 3, Article 6, 7 p. (2008; Zbl 1186.60009) Full Text: arXiv Link
Bilyk, Dmitriy; Lacey, Michael T. On the small ball inequality in three dimensions. (English) Zbl 1202.42007 Duke Math. J. 143, No. 1, 81-115 (2008). Reviewer: Robert F. Tichy (Graz) MSC: 42A05 11K38 PDFBibTeX XMLCite \textit{D. Bilyk} and \textit{M. T. Lacey}, Duke Math. J. 143, No. 1, 81--115 (2008; Zbl 1202.42007) Full Text: DOI arXiv
Bilyk, Dmitriy; Lacey, Michael T.; Vagharshakyan, Armen On the small ball inequality in all dimensions. (English) Zbl 1214.42024 J. Funct. Anal. 254, No. 9, 2470-2502 (2008). MSC: 42B25 11K38 46E30 41A46 46B99 60E15 PDFBibTeX XMLCite \textit{D. Bilyk} et al., J. Funct. Anal. 254, No. 9, 2470--2502 (2008; Zbl 1214.42024) Full Text: DOI arXiv