Dr. Jonas Jankauskas

Postdoctoral Fellow

Mathematik und Statistik
Montanuniversität Leoben
Franz Josef Straße 18
A-8700 Leoben
Austria


My Vita [EN] [LT] Research Statement Teaching Statement Complete List of Publications Doctoral thesis 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 at Simon Fraser University and years 2014-2015 at the University of Waterloo as a postdoc. As of 2016, I moved to MU Leoben in Austria. My Erdős number is 3.

Research

During my doctoral studies, I studied 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 their extremal properties, the divisibility and the zero sets of polynomials. I was interested in various arithmetic, algebraic and geometric properties of roots of polynomials that depend on heights. As a postdoc, I investigated the distribution of fractional parts of powers of Pisot numbers, linear relations between the conjugates of algebraic numbers and interlacing patterns that occur in the correspondence problem between Pisot and Salem numbers. My current research at MU Leoben is focused on almost linear dynamical systems and fractals associated to the number systems.

Papers & Preprints

21.Binary words, winding numbers and polynomials with interlaced roots, (submitted).
20.Characterization of rational matrices that admit finite digit systems, Linear Algebra and its Applications, 557 (2018), 350--358. (with J. Thuswaldner)
19.On certain multiples of Littlewood and Newman polynomials, Bull. Korean Math. Soc., 5 (55) 1491--1501. (with P. Drungilas, L. Klebonas and G. Junevičius)
18.On Littlewood and Newman polynomial multiples of Borwein polynomials, Mathematics of Computation, 87 (311) (2018), 1523--1541. (with P. Drungilas and J. Šiurys)
17.No two non-real conjugates of a Pisot number have the same imaginary part, Mathematics of Computation, 86 (304) (2017), 335--350. (with A. Dubickas and K. G. Hare)
16.On linear relations between conjugate algebraic numbers of low degree, Journal of the Ramanujan Mathematical Society, 30 (2) (2015) 219--235. (with A. Dubickas)
15.On Littlewood polynomials with prescribed number of zeros inside the unit disk, Canadian Journal of Mathematics, 67 (3) (2015) 507--526. (with P. Borwein, S. Choi and R. Ferguson)
14.On fractional parts of powers of Pisot numbers of length at most 4, Journal of Number Theory, 144 (2014) 325--339. (with A. Dubickas)
13. On relations for rings generated by algebraic numbers and their conjugates, Annali di Matematica Pura ed Applicata, 194 (2) (2015) 369--385. (with P. Drungilas and A. Dubickas)
12. Extremal Mahler measures and Ls norms in the class of polynomials related to Barker sequences, Proceedings of the American Mathematical Society, 141 (8) (2013) 2653--2663. (with P. Borwein and S. K. K. Choi)
11. Nonreciprocal algebraic numbers of small Mahler's measure, Acta Arithmetica, 157 (4) (2013) 357--364. (with A. Dubickas)
10. Height reducing problem on algebraic integers, Functiones et Approximatio Commentarii Mathematici, 47 (1) (2012), 105--119. (with S. Akiyama and P. Drungilas)
9. On a class of polynomials related to Barker sequences, Proceedings of the American Mathematical Society, 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, Journal of the Australian Mathematical Society, 92 (2012), 155--161. (with H. Ganguli).
7. The t-metric Mahler measures of surds of rational numbers, Acta Mathematica Hungarica, 134 (4) (2012), 481--498. (with C. L. Samuels)
6. On the intersection of infinite geometric and arithmetic progressions, Bulletin of the Brazilian Mathematical Society, 41 (4) (2010), 551--566. (with A. Dubickas)
5. On Mahler measures of a self-inversive polynomial and its derivative, Bulletin of the London Mathemetical Society, 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, Publicationes Mathematicae Debrecen , 17 (3-4) (2007), 325--348. (with A. Dubickas)

Talks

Conferences and visits

Useful Links

My collaborators Websites and resources
Shigeki Akiyama Number Theory Web
Peter Borwein MIFMO
Stephen Choi Mathematics Genealogy Project
Artūras Dubickas MathJobs.org
Paulius Drungilas MathSciNet
Kevin G. Hare Lietuvos Jaunųjų Matematikų Susitikimas
Charles Samuels CV Template
Jonas Šiurys
Jörg Thuswaldner