Jonas Jankauskas Homepage

Dr. Jonas Jankauskas

Postdoctoral Fellow

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

jonas.jankauskas@gmail.com

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 L^s 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 L_s 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)h^m(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)

Contributed Talks

{0,1} and {−1,1} -- polynomials with prescribed number of zeros inside disk, slides
Skaičiavimo sistemos, kurių bazės matrica turi tikrinių reikšmių ant vienetinio apskritimo (in Lithuanian), slides
On Littlewood and Newman polynomial multiples of Borwein polynomials, slides
Pisot-Salem numbers, interlacing and {0,1}-words, slides
Simple linear relations between conjugate algebraic numbers, slides
Tiesinės lygtys jungtiniams algebriniams skaičiams (in Lithuanian) slides
On Littlewood polynomials with prescribed number of zeros inside the unit disk, slides
Thesis defense presentation, slides (in Lithuanian), photos
Polinomai ir Barkerio sekos, LMD J. Kubiliaus seminaras slides (in Lithuanian)
On a class of polynomials related to Barker sequences, slides
On the intersection of infinite geometric and arithmetic progressions, slides
On Newman polynomials which divide no Littlewood polynomial, slides

Conferences and visits

9-asis Lietuvos jaunųjų matematikų susitikimas (online) December 28 2020.
8-asis Lietuvos jaunųjų matematikų susitikimas, Kaunas Technology University, Kaunas, December 27 2019.
Weekly Seminar of Faculty of Informatics, Debrecen University (guest speaker), Debrecen University, Faculty of Informatics, Debrecen, October 2 2019.
Worskhop on number systems in lattices (invited speaker), Eötvös Loránd University, Faculty of Informatics, Budapest, September 25 2019.
7-asis Lietuvos jaunųjų matematikų susitikimas, Vilnius University, Vilnius, December 28 2018.
ANTS XIII, University of Wisconsin, Madison, July 16-20 2018.(photo)
CNTA XV, Université Laval, Quebec City, July, 9-13 2018. [abstract] (photo)
Seminar der Lehrstuhl für Mathematik und Statistik , Montanuniversität Leoben, Leoben, June 6-8 2018.
Numeration 2018, Université Paris Diderot(Paris 7), Paris, May 22-25 2018. [abstract]
6-asis Lietuvos jaunųjų matematikų susitikimas, Kaunas Technology University, Kaunas, December 29 2017.
Vilnius Conference in Combinatorics and Number Theory, Vilnius University, Vilnius, July 16-22 2017. [abstract]
30th Journées Arithmétiques, University of Caen, Caen, Normandy, July 3-7 2017. [abstract] (photo)
Numeration 2017, Roma Tre University in Rome, June 5-9 2017. [abstract]
5-asis Lietuvos jaunųjų matematikų susitikimas, Vilnius Tech Park, Vilnius, 29 December 2016.
Numeration 2016, Czech Technical University in Prague, Prague, May 23-27 2016. [abstract] (photos)
Sage Days 72, Czech Technical University in Prague, Prague, May 21-22 2016.
4-asis Lietuvos jaunųjų matematikų susitikimas, Vilnius University, Vilnius, 2 January 2016. (photos)
29th Journées Arithmétiques and Kálmán Győry 75 Symposium, Debrecen, Hungary, July 6-11, 2015. [abstracts] (photos)
AMMCS-CAIMS 2015, Wilfrid Loriel University , Waterloo, Ontario, Canada, June 7-12, 2015. [abstract]
3-iasis Lietuvos jaunųjų matematikų susitikimas, KTU University, Kaunas, 2 January 2015 sausio 2. (photos)
CNTA XIII, Carleton University, Ottawa, June 16-20, 2014, [abstract]
2014 CMS Summer Meeting, Winnipeg, Manitoba, Canada, June 6-9, 2014, [abstract] (photos)
PNWNTC 2014, Burnaby BC, Canada, May 17-18, 2014 (photos)
PNWNTC 2013, Seattle, USA, June 1-2, 2013 (photos)
27th Journées Arithmétiques, Vilnius, Lithuania, June 27-July 1, 2011. [abstract] (photos)
Heights 2011, Tossa de Mar, Spain, April 25-30, 2011, (photos) [abstract]
Research visit to Peter Borwein at IRMACS, Simon Fraser University. Burnaby, British Columbia, Canada, September 1, 2010 - January 30, 2011. (photos)
PIMS/SFU/UBC Number Theory Seminar, October 7, 2010
19th Czech and Slovak International Conference on Number Theory, Hradec nad Moravicí, Czech Republic, August 31-September 4, 2009. (photo)
Winter School On Explicit Methods in Number Theory , Institute of Mathematics, Univercity of Debrecen, Debrecen, Hungary, January 26-30, 2009
Number Theory seminar, The School of Mathematics, University of Edinburgh (a visit to Chris Smyth), Edinburgh, Scotland, November 2-8 2008
Journée Diophantienne , L'Institut de Recherche Mathématique Avancée, L’Université de Strasbourg, Strasbourg, France, October 20-25, 2008
International Conference on Number Theory, dedicated to the 60th birthday of A.Laurinčikas, Šiauliai, Lithuania, August 11-15, 2008

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

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 L_s 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)h^m(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)