2024
Hančl, J., Nair, R., & Verger-Gaugry, J. -L. (2024). On polynomials in primes, ergodic averages and monothetic groups. Monatshefte für Mathematik. doi:10.1007/s00605-024-01948-0DOI: 10.1007/s00605-024-01948-0
2022
Nair, R., & Haddley, A. (n.d.). On Schneider’s Continued Fraction Map on a Complete Non-Archimedean Field. Arnold Mathematical Journal. doi:10.1007/s40598-021-00190-yDOI: 10.1007/s40598-021-00190-y
2021
Nair, R., Verger-Gaugry, J. -L., & Weber, M. (2021). On good universality and the Riemann Hypothesis. ADVANCES IN MATHEMATICS, 385. doi:10.1016/j.aim.2021.107762DOI: 10.1016/j.aim.2021.107762
2020
Nair, R., & Nasr, E. (2020). On uniform distribution of polynomials and good universality. Ergodic Theory and Dynamical Systems, 40(4), 992-1007. doi:10.1017/etds.2018.53DOI: 10.1017/etds.2018.53
2019
Nair, R., Karpenkov, O., & Verger-Gaugry, J. -L. (2019). The Sixth International Conference on Uniform Distribution Theory (UDT 2018) CIRM, Luminy, Marseilles, France, October 1–5, 2018.. Uniform Distribution Theory. doi:10.2478/UDT-2019–0009DOI: 10.2478/UDT-2019–0009
2018
Nair, R., Hancl, J., & Kolouch, O. (2018). Irrationality and transcendence of infinite continued fraction expansions. Acta Arithmetica.
Lertchoosakul, P., & Nair, R. (2018). ON THE QUANTITATIVE METRIC THEORY OF CONTINUED FRACTIONS IN POSITIVE CHARACTERISTIC. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 61(1), 283-293. doi:10.1017/S0013091517000177DOI: 10.1017/S0013091517000177
2017
Nair, R., & Ma, L. (2017). Haas-Molnar Continued Fractions and Metric Diophantine Approximation.. Труды Математического Института имени В. / Proceedings of the Steklov Institute of Mathematics / Trudy Matematicheskogo Instituta imeni V.A. Steklova, 299, 157-177. doi:10.1134/S0081543817080119DOI: 10.1134/S0081543817080119
Ma, L., & Nair, R. (2017). Limit theorems for sub-sums of partial quotients of continued fractions. Indagationes Mathematicae, 28(5), 913-927. doi:10.1016/j.indag.2017.06.006DOI: 10.1016/j.indag.2017.06.006
Hancl, J., & Nair, R. (2017). ON THE IRRATIONALITY OF INFINITE SERIES OF RECIPROCALS OF SQUARE ROOTS. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 47(5), 1525-1538. doi:10.1216/RMJ-2017-47-5-1525DOI: 10.1216/RMJ-2017-47-5-1525
Haddley, A., Lertchoosakul, P., & Nair, R. (2017). The Halton sequence and its discrepancy in the Cantor expansion. PERIODICA MATHEMATICA HUNGARICA, 75(1), 128-141. doi:10.1007/s10998-016-0169-5DOI: 10.1007/s10998-016-0169-5
2016
On Variants of the Halton Sequences (Journal article)
Jassova, A., Lertchoosakul, P., & Nair, R. (2016). On Variants of the Halton Sequences. Monatshefte fuer Mathematik, 180, 743-764. doi:10.1007/s00605-015-0794-8DOI: 10.1007/s00605-015-0794-8
Jassova, A., Lertchoosakul, P., & Nair, R. (2016). On variants of the Halton sequence. MONATSHEFTE FUR MATHEMATIK, 180(4), 743-764. doi:10.1007/s00605-015-0794-8DOI: 10.1007/s00605-015-0794-8
Nair, R., & Nasr, E. (2016). Pair Correlations and Random Walks on the Integers. Uniform distribution theory, 11(1), 159-164. doi:10.1515/udt-2016-0008DOI: 10.1515/udt-2016-0008
Quantitative metric theory of continued fractions (Journal article)
Hancl, J., Haddley, A., Lertchoosakul, P., & Nair, R. (2016). Quantitative metric theory of continued fractions. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 126(2), 167-177. doi:10.1007/s12044-016-0266-7DOI: 10.1007/s12044-016-0266-7
2015
Nair, R. (2015). On moving averages and asymptotic equipartition of information. PERIODICA MATHEMATICA HUNGARICA, 71(1), 59-63. doi:10.1007/s10998-014-0080-xDOI: 10.1007/s10998-014-0080-x
Kristensen, S., Jassova, A., Lertchoosakul, P., & Nair, R. (2015). On Poincare recurrence in positive characteristic. Indagationes Mathematicae, 26(2), 346-354. doi:10.1016/j.indag.2014.11.003DOI: 10.1016/j.indag.2014.11.003
2014
On expressible sets of products (Journal article)
Hancl, J., Nair, R., & Novotny, L. (2014). On expressible sets of products. PERIODICA MATHEMATICA HUNGARICA, 69(2), 199-206. doi:10.1007/s10998-014-0058-8DOI: 10.1007/s10998-014-0058-8
A remark on the distribution of Chebychev polynomials on [-1,1]. (Journal article)
Chan, K., & Nair, R. (2014). A remark on the distribution of Chebychev polynomials on [-1,1].. Uniform Distribution Theory, 9(2), 125-134. Retrieved from https://math.boku.ac.at/udt/
ON THE COMPLEXITY OF THE LIOUVILLE NUMBERS IN POSITIVE CHARACTERISTIC (Journal article)
Lertchoosakul, P., & Nair, R. (2014). ON THE COMPLEXITY OF THE LIOUVILLE NUMBERS IN POSITIVE CHARACTERISTIC. The Quarterly Journal of Mathematics, 65(2), 439-457. doi:10.1093/qmath/hat019DOI: 10.1093/qmath/hat019
Chan, K., & Nair, R. (2014). Problems in Strong Uniform Distribution. Tatra Mountains Mathematical Publications, 59(1), 51-64. doi:10.2478/tmmp-2014-0018DOI: 10.2478/tmmp-2014-0018
ON THE COMPLEXITY OF THE LIOUVILLE NUMBERS IN POSITIVE CHARACTERISTIC (Journal article)
Lertchoosakul, P., & Nair, R. (2014). ON THE COMPLEXITY OF THE LIOUVILLE NUMBERS IN POSITIVE CHARACTERISTIC. QUARTERLY JOURNAL OF MATHEMATICS, 65(2), 439-457. doi:10.1093/qmath/hat019DOI: 10.1093/qmath/hat019
On the metric theory of continued fractions in positive characteristic (Journal article)
Lertchoosakul, P., & Nair, R. (2014). On the metric theory of continued fractions in positive characteristic. Mathematika, 60(2), 307-320. doi:10.1112/S0025579314000114DOI: 10.1112/S0025579314000114
2013
Distribution functions for subsequences of the van der Corput sequence (Journal article)
Lertchoosakul, P., & Nair, R. (2013). Distribution functions for subsequences of the van der Corput sequence. Indagationes Mathematicae, 24(3), 593-601. doi:10.1016/j.indag.2013.03.006DOI: 10.1016/j.indag.2013.03.006
Optimal continued fractions and the moving average ergodic theorem (Journal article)
Haili, H. K., & Nair, R. (2013). Optimal continued fractions and the moving average ergodic theorem. Periodica Mathematica Hungarica, 66(1), 95-103. doi:10.1007/s10998-012-7874-5DOI: 10.1007/s10998-012-7874-5
Optimal continued fractions and the moving average ergodic theorem (Journal article)
Kamarul-Haili, H., & Nair, R. (2013). Optimal continued fractions and the moving average ergodic theorem. Periodica Mathematica Hungarica, 66(1), 95-103.
On polynomial actions in positive characteristic (Journal article)
Hancl, J., Jassova, A., Lertchoosakul, P., & Nair, R. (2013). On polynomial actions in positive characteristic. Proceedings of the Steklov Institute of Mathematics (Supplementary Issues), 280(Supple), 37-42.
On the metric theory of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>p</mml:mi></mml:math>-adic continued fractions (Journal article)
Hančl, J., Jaššová, A., Lertchoosakul, P., & Nair, R. (2013). On the metric theory of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>p</mml:mi></mml:math>-adic continued fractions. Indagationes Mathematicae, 24(1), 42-56. doi:10.1016/j.indag.2012.06.004DOI: 10.1016/j.indag.2012.06.004
On the nearest integer continued fraction expansion and moving average ergodic theorem (Journal article)
Kamarul-Haili, H., & Nair, R. (2013). On the nearest integer continued fraction expansion and moving average ergodic theorem. Uniform Distribution Theory, 8(1), 73-87.
2012
On Templeman averages and variation functions (Journal article)
Nair, R. (2012). On Templeman averages and variation functions. Periodica Mathematica Hungarica, 64(1), 39-51. doi:10.1007/s10998-012-9039-yDOI: 10.1007/s10998-012-9039-y
On the Hausdorff dimension of the expressible set of certain sequences (Journal article)
Hancl, J., Nair, R., Novotny, L., & Sustek, J. (2012). On the Hausdorff dimension of the expressible set of certain sequences. Acta Arithmetica, 155, 85-90.
Polynomial actions in positive characteristic (Journal article)
Hancl, J., Jassova, A., Lertchoosakul, P., & Nair, R. (2012). Polynomial actions in positive characteristic. Proceeds of The Steklov Institute. Suplement, 7 pp.
Polynomial actions in positive characteristic (Journal article)
Hancl, J., Jassova, A., Lertchoosakul, P., & Nair, R. (2012). Polynomial actions in positive characteristic. Sovremennye Problemy Matematiki, (16), 45-51. Retrieved from http://www.mathnet.ru/links/5934de68ea9520988d8c2a9b5acbd1e4/book1451.pdf
The nearest integer continued fraction transformation and the moving average ergodic theorem (Journal article)
Haili Kamarul, H., & Nair, R. (2012). The nearest integer continued fraction transformation and the moving average ergodic theorem. Uniform Distribution Theory.
2011
On general densities and intersectivity (Journal article)
Nair, R. (2011). On general densities and intersectivity. Indagationes Mathematicae, 22(1-2), 131-134. doi:10.1016/j.indag.2011.08.007DOI: 10.1016/j.indag.2011.08.007
On moving averages and continued fractions (Journal article)
Kamarul Haili, H., & Nair, R. (2011). On moving averages and continued fractions. Uniform Distribution Theory, 6(1), 65-78.
2010
On expressible sets and p-adic numbers (Journal article)
Hancl, J., Nair, R., Pulcerova, S., & Sustek, J. (2010). On expressible sets and p-adic numbers. Proceedings of The Edinburgh Math Society, 53, 1-12.
On moving averages and continued fractions (Journal article)
Kamarul-Haili, H., & Nair, R. (2010). On moving averages and continued fractions. Uniform Distribution Theory, 6(1), 65-78.
2009
On pair correlations and Hausdorff dimension (Journal article)
Nair, R. (2009). On pair correlations and Hausdorff dimension. Israel Journal of Mathematics, 171(1), 197-219. doi:10.1007/s11856-009-0047-4DOI: 10.1007/s11856-009-0047-4
On an arithmetic limit on compact groups (Journal article)
Nair, R. (2009). On an arithmetic limit on compact groups. Uniform Distribution Theory, 2, 39-45.
2008
Pair correlation of the LeVeque Sequence on the polydisc (Journal article)
Nair, R. (2008). Pair correlation of the LeVeque Sequence on the polydisc. Mathematical Proceedings of The Cambridge Philosophical Society, 145(1), 197-203.
Pair correlations of the leVeque sequence on the polydisc (Journal article)
NAIR, R. (2008). Pair correlations of the leVeque sequence on the polydisc. Mathematical Proceedings of the Cambridge Philosophical Society, 145(1), 197-203. doi:10.1017/s0305004108001229DOI: 10.1017/s0305004108001229
Numbers and Polynomials (Conference Paper)
McKey, J., & Smyth, C. (Eds.) (2008). Numbers and Polynomials. In Numbers and Polynomials (pp. 241-254). Bristol: London Mathematical Society.
Polynomial ergodic averages and square functions (Chapter)
Nair, R. (2008). Polynomial ergodic averages and square functions. In J. McKee, C. Smyth, & N. J. Hitchin (Eds.), Number Theory and Polynomials (Vol. 352, pp. 241-254). Cambridge: Cambridge University Press.
``On summability to arbitrary real numbers'' (Journal article)
Bodyagin, D., Hancl, J., Nair, R., Rucki, P., & Sustek, J. (2008). ``On summability to arbitrary real numbers''. Elemente Der Mathematik, 63(1), 30-34.
2007
On Vector Valued Ergodic Theorems (Journal article)
Nair, R. (2007). On Vector Valued Ergodic Theorems. Tetra Mountain Mathematical Publications.
Pair correlations of sequences in higher dimensions (Journal article)
Nair, R., & Pollicott, M. (2007). Pair correlations of sequences in higher dimensions. Israel Journal of Mathematics, 157(1), 219-238. doi:10.1007/s11856-006-0009-zDOI: 10.1007/s11856-006-0009-z
2006
On the Lebesgue measure of the expressible set of certain sequences (Journal article)
Hančl, J., Nair, R., & Šustek, J. (2006). On the Lebesgue measure of the expressible set of certain sequences. Indagationes Mathematicae, 17(4), 567-581. doi:10.1016/s0019-3577(06)81034-7DOI: 10.1016/s0019-3577(06)81034-7
An Exceptional Set in the Ergodic Theory of Expanding Maps on Manifolds (Journal article)
Abercrombie, A. G., & Nair, R. (2006). An Exceptional Set in the Ergodic Theory of Expanding Maps on Manifolds. Monatshefte für Mathematik, 148(1), 1-17. doi:10.1007/s00605-005-0391-3DOI: 10.1007/s00605-005-0391-3
2005
On strong uniform distribution VI (Journal article)
Nair, R. (2005). On strong uniform distribution VI. Journal of Inequalities and applications, 2005(3), 319-327.
2004
On random perturbation of some intersective sets (Journal article)
Nair, R., & Weber, M. (2004). On random perturbation of some intersective sets. Indagationes Mathematicae, 15(3), 373-381. doi:10.1016/s0019-3577(04)80006-5DOI: 10.1016/s0019-3577(04)80006-5
2003
On uniformly distributed sequences of integers and Poincaré recurrence III (Journal article)
Nair, R. (2003). On uniformly distributed sequences of integers and Poincaré recurrence III. Bulletin of the Australian Mathematical Society, 68(2), 345-350. doi:10.1017/s0004972700037722DOI: 10.1017/s0004972700037722
On certain Glasner sets (Journal article)
Haili, H. K., & Nair, R. (2003). On certain Glasner sets. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 133(4), 849-853. doi:10.1017/s0308210500002705DOI: 10.1017/s0308210500002705
On strong uniform distribution III (Journal article)
Nair, R. (2003). On strong uniform distribution III. Indagationes Mathematicae, 14(2), 233-240. doi:10.1016/s0019-3577(03)90007-3DOI: 10.1016/s0019-3577(03)90007-3
On a problem of R. C. Baker (Journal article)
Nair, R. (n.d.). On a problem of R. C. Baker. Acta Arithmetica, 109(4), 343-348. doi:10.4064/aa109-4-4DOI: 10.4064/aa109-4-4
The discrepancy of some real sequences (Journal article)
Haili, H. K., & Nair, R. (n.d.). The discrepancy of some real sequences. MATHEMATICA SCANDINAVICA, 93(2), 268. doi:10.7146/math.scand.a-14423DOI: 10.7146/math.scand.a-14423
2002
On the Hausdorff dimension of certain self-affine sets (Journal article)
Abercrombie, A. G., & Nair, R. (n.d.). On the Hausdorff dimension of certain self-affine sets. Studia Mathematica, 152(2), 105-124. doi:10.4064/sm152-2-1DOI: 10.4064/sm152-2-1
2001
On certain sets of integers and intersectivity (Journal article)
NAIR, R., & ZARIS, P. (2001). On certain sets of integers and intersectivity. Mathematical Proceedings of the Cambridge Philosophical Society, 131(01). doi:10.1017/s0305004101005059DOI: 10.1017/s0305004101005059
On Strong Uniform Distribution II (Journal article)
Nair, R. (2001). On Strong Uniform Distribution II. Monatshefte für Mathematik, 132(4), 341-348. doi:10.1007/pl00010091DOI: 10.1007/pl00010091