Dr. Jonas Jankauskas

Postdoctoral Fellow

Department of Pure Mathematics
University of Waterloo


200 University Avenue West
Waterloo, Ontario
Canada V2L 3G1

Office: MC 4032


My Vita Research Statement Teaching Statement Complete List of Publications Doctoral thesis (EN) Thesis Summary (LT)

About me

I am doing mathematical research and teaching students since 2005 - see my CV for details. I finished my PhD studies in mathematics at Vilnius University under the supervision of Artūras Dubickas and successfully defended doctoral thesis Heights of Polynomials. I spent the year 2013 as a postdoc at Simon Fraser University. Since 2014, I am a postdoc at University of Waterloo. My Erdős number is 3.

Research

I am interested how the different heights of polynomials P(x) (the naive height H(P), the length L(P), the number of nonzero terms, the Mahler measure M(P), the Ls norm ||P||s) affect the extremal properties, the divisibility and the zeros of polynomials. I study various arithmetic, algebraic and geometric properties of roots of polynomials that depend on the heights of P(x). More recently, I did a research on combinatorics of words that represent the interlaced roots of polynomials and the construction of Littlewood polynomials with prescribed number of roots inside the disk. Also, I investigated the distribution of fractional parts of powers of Pisot numbers of small length and arithmetical relations that occur between the conjugates of algebraic numbers.

Papers (published, accepted and submitted)

18.There are no two non-real conjugates of a Pisot number with the same imaginary part, (submitted). (with A. Dubickas, K. G. Hare)
17.Simple linear relations with conjugate algebraic numbers of low degree, (submitted). (with A. Dubickas)
16.Binary words, winding numbers and polynomials with interlaced roots, (submitted).
15.On fractional parts of powers of Pisot numbers of length at most 4, J. of Number Theory, (to appear). (with A. Dubickas)
14.On Littlewood polynomials with prescribed number of zeros inside the unit disk, Canad. J. Math., (to appear). (with P. Borwein, S. Choi and R. Ferguson)
13. On relations for rings generated by algebraic numbers and their conjugates, Ann. Mat. Pura Appl., (to appear). (with A. Dubickas and P. Drungilas)
12. Extremal Mahler measures and Ls norms in the class of polynomials related to Barker sequences, Proceedings of Amer. Math. Soc., 141 (8) (2013) 2653--2663. (with P. Borwein and S. K. K. Choi)
11. Nonreciprocal algebraic numbers of small Mahler's measure, Acta Arith., 157 (4) (2013) 357--364. (with A. Dubickas)
10. Height reducing problem on algebraic integers, Funct. Approx. Comment. Math. 47 (1) (2012), 105--119. (with S. Akiyama and P. Drungilas)
9. On a class of polynomials related to Barker sequences, Proceedings of Amer. Math. Soc., 140 (8) (2012), 2613--2625.(with P. Borwein and S. Choi)
8. On the equation f(g(x)) = f(x)hm(x) for composite polynomials, J. Aust. Math. Soc. 92 (2012), 155--161. (with H. Ganguli).
7. The t-metric Mahler measures of surds of rational numbers, Acta Math. Hungar., 134 (4) (2012), 481--498. (with C. L. Samuels)
6. On the intersection of infinite geometric and arithmetic progressions, Bull. of the Brazilian Math. Soc., 41 (4) (2010), 551--566. (with A. Dubickas)
5. On Mahler measures of a self-inversive polynomial and its derivative, Bull. London Math. Soc., 42 (2) (2010), 195--209. (with A. Dubickas)
4. On the reducibility of certain quadrinomials, Glasnik Matematički, 45 (65) (2010), 31--41.
3. On Newman polynomials which divide no Littlewood polynomial, Mathematics of Computation, 78 (265) (2009), 327--344.(with A. Dubickas)
2. The maximal value of polynomials with restricted coefficients, Journal of the Korean Mathematical Society, 46 (1) (2009), 41--49.(with A. Dubickas)
1. On the reduced height of a polynomial, Publ. Math. Debrecen , 17 (3-4) (2007), 325--348.(with A. Dubickas)

Talks

Conferences and visits

Useful Links

My Collaborators Mathematical Websites
Shigeki Akiyama Number Theory Web
Peter Borwein MIFMO
Stephen Choi Mathematics Genealogy Project
Artūras Dubickas MathJobs.org
Paulius Drungilas MathSciNet
Himadri Ganguli
Charles Samuels