Papers
 Finite subsets of integer lattice in the plane
and friendly paths. The full solution of American Mathematical Monthly Problem 11484 (b)*.
The Minkowski question mark function, and topics related to continued fractions, modular world
 Transfer operator for the Gauss' continued fraction map. I. Structure of the eigenvalues and trace formulas. The newest version.
The talk on this topic given in February, 2015.

The modular group and words in its two generators,
Lith. Math. J. 57 (1) (2017), 112;
Official LINK.

The Minkowski ?(x), a class of singular measures, quasimodular and meanmodular forms. I. The newest version.
"The Minkowski question mark function, quasimodular forms and the Dedekind etafunction",
the talk on this topic given in March, 2017.

The map from the set of nontrivial zeros of the Riemann zeta function to the set of eigenvalues
of the GaussKuzminWirsing operator.
 FourierStieltjes coefficients of the Minkowski question mark function,
Anal. Probab. Methods Number Theory, Proceedings of the Fifth Intern. Conf. in Honour of J. Kubilius, Palanga, Lithuania,
410 September 2011 (2012), 1933.
 The Minkowski ?(x) function and Salem's problem,
Comptes Rendus Mathématique 350 (34) (2012), 137140.

Semiregular continued fractions and an exact formula for the moments of the Minkowski question mark function,
Ramanujan J. 25 (3) (2011), 359367; Official LINK.

The Minkowski question mark function: explicit series for the dyadic period function and moments,
Math. Comp. 79 (269) (2010), 383418;
Addenda and corrigenda, Math. Comp. 80 (276) (2011), 24452454.
 The moments of Minkowski question mark function: the dyadic period function,
Glasg. Math. J. 52 (1) (2010), 4164.
 Generating and zeta functions, structure, spectral and analytic properties
of the moments of the Minkowski question mark function, Involve 2 (2) (2009), 121159.
 An asymptotic formula for the moments of Minkowski question mark function
in the interval [0,1], Lith. Math. J. 48 (4) (2008), 357367; Official LINK.
Projective and general flows: relations to topology, algebraic geometry, differential geometry, differential equations and mathematical physics
 Projective and polynomial superflows. I.
Latest version is here (110 pages).
 Projective and polynomial superflows. II. O(3) and the icosahedral group.
 Projective and polynomial superflows. III. Finite subgroups of U(2).
 Beltrami vector fields with polyhedral symmetries.
 Beltrami vector fields with an icosahedral symmetry,
Journal of Geometry and Physics. Article 103655, July (153) (2020), 14 p.; Official LINK.
 Planar 2homogeneous commutative rational vector fields, Electron. J. Differential Equations. Vol. 2018 (2018), No. 138, pp. 121; Official LINK.
 The projective translation equation and rational plane flows. II. Corrections and additions,
Aequationes Math. 91 (5) (2017), 871907;
Official LINK.
 Algebraic and abelian solutions to the projective translation equation, Aequationes Math.
90 (4) (2016), 727763;
Official LINK.
 The projective translation equation
and unramified 2dimensional flows with rational vector fields, Aequationes Math.
89 (3) (2015), 873913;
Official LINK.
 The projective translation equation and rational plane flows. I, Aequationes Math.
85 (3) (2013), 273328;
Official LINK.
 Multivariable translation equation which arises from homothety, Aequationes Math.
80 (3) (2010), 335350;
Official LINK.
Other: number theory, partitions
 mnariniai skaidiniai, (1999). Coursework. This paper, written in Lithuanian, contains new proof of a known theorem, and some new results. In particular, it gives the first ever characterization of mary partitons modulo m, which was rediscovered 16 years later in the paper in American Mathematical Monthly. See the webpage of
Doron Zeilberger.
 Algebraic functions with Fermat property, eigenvalues of transfer operator and Riemann zeros, and other open problems.
 Congruence properties of the function that counts compositions into powers of 2,
J. Integer Seq. 13 (2010), Article: 10.5.3, 9 p.
 A curious proof of Fermat's little theorem, Amer. Math. Monthly 116 (4) (2009), 362364;
Official LINK.
 Functional equation related to
quadratic and norm forms, Lith. Math. J. 45 (2) (2005), 153172;
Official LINK.
 Prime and composite numbers as integer
parts of powers (with A. Dubickas), Acta Math. Hungar. 105 (3) (2004), 249256;
Official LINK.
 Dirichlet series associated with strongly
qmultiplicative functions, Ramanujan J. 8 (1) (2004), 1321.
Official LINK.
 Generalization of the RödsethGupta
theorem on binary partitions, Lith. Math. J. 43 (2) (2003), 123132;
Official LINK.
Ph.D. thesis:
"Integral transforms of the Minkowski question mark function" (2008).
Popular papers, notes
 Author of IMO 6, 1997, "American Mathematical Monthly" problems 11484, 11661,
coauthor of IMO 3, 2008.
 The moments of the Minkowski question mark function, MinkowskiAlkauskas constants by Steven R. Finch,
and
here.
 Author of the sequences A265434 and A220420 in "The OnLine Encyclopedia of Integer Sequences".
 Friendly paths
(solution of the problem 11484) Amer. Math. Monthly 119 (2) (2012), 167168.
(The official solution contains few typos: ba1 and ba+2 should be replaced by
ba and ba+1 in the displayed inequality);
Official LINK.
 Recursive construction of a series converging to the
eigenvalues of the GaussKuzminWirsing operator, (2010). This paper is not for publication since it was superseded by
this paper.
 Dirichlet series associated with
ThueMorse sequence; Vilnius University, Department of Mathematics, preprint (2001). This contains the explicit construction of the function F(x) which satisfies
F'(x)=4F(2x). This very function, called Fabius function, was independently rediscovered by many researchers.
 Exact lower bound for the house of algebraic integer with abelian Galois group
(2003). The result of the note is a rediscovery of the old result of A. Schinzel.
 Splitting of primes in Q(^{5}v2) , tutorial
(2004); inspired by the excellent introduction to algebraic number theory by H. Stark.
 A question from complex dynamics (2008).
 Solutions of IMO 2005.
 Prime numbers in arithmetic progressions, Alfa+Omega 2 (4), 4 pages, (1997).
 The germs of important mathematical results in pupil olympiads, Alfa+Omega 2 (4), 5 pages, (1997).
 Inequalities, Alfa+Omega 1 (5), 6 pages, 1998.
 Functional equations in pupil olympiads, Alfa+Omega 1 (7), 14 pages, (1999).
 Commutative polynomials, Alfa+Omega 1 (7), 4 pages, (2001).
 Several brochures (with coauthors) on
Lithuanian Mathematical Olympiads, 19962000.