Digital expansions of natural numbers are used in many different areas
of mathematics (to say nothing of the binary representation of
numbers in every computer). Especially they occur in various algorithms,
e.g. for computing powers with large exponents, and for generating
random numbers. Therefore there is a demand for investigating statistical
properties of digital expansions. This research project aims at
applications as well as at theoretical aspects, most of which are of a
numbertheorical nature.
Most of our methods come from combinatorics, analytic number theory,
complex analysis, and probability theory. Digital expansions based
on linear recursions surprisingly raise geometric questions concerning
dynamical processes generated by torus automorphisms.
Selected Publications:
M. Drmota and J. Gajdosik.
The distribution of the sumofdigits
function.
J. Théor. Nombres Bordeaux 10/1 (1998), 1732.
[MR].
M. Drmota and J. Gajdosik.
The parity of the sumofdigitsfunction of
generalized Zeckendorf representations.
Fibonacci Quart. 36/1 (1998), 319.
[MR].
M. Drmota and M. Skalba.
Rarified sums of the ThueMorse
sequence.
Trans. Amer. Math. Soc. 352/2 (2000), 609642.
[MR].
M. Drmota and M. Skalba.
The parity of the Zeckendorf sumofdigits
function.
Manuscripta Math. 101/3 (2000), 361383.
[MR].
M. Drmota.
The distribution of patterns in digital
expansions.
In F. HalterKoch and R. F. Tichy, editors, Algebraic number theory and
Diophantine analysis (Graz, 1998), pages 103121. de Gruyter, Berlin,
2000.
[MR].
M. Drmota and G. Larcher.
The sumofdigitsfunction and uniform
distribution modulo 1.
J. Number Theory 89/1 (2001), 6596.
[MR].
M. Drmota.
The joint distribution of qadditive
functions.
Acta Arith. 100/1 (2001), 1739.
[MR].
W. Steiner.
Parry expansions of
polynomial sequences.
Integers 2 (2002), Paper A14, 28 pp. (electronic).
[MR], [pdf].
M. Fuchs.
Digital expansion of exponential
sequences.
J. Théor. Nombres Bordeaux 14/2 (2002), 477487.
[MR], [pdf].
M. Drmota and W. Steiner.
The Zeckendorf expansion of polynomial
sequences.
J. Théor. Nombres Bordeaux 14/2 (2002), 439475.
[MR], [pdf].
M. Fuchs.
On metric Diophantine approximation in
the field of formal Laurent series.
Finite Fields Appl. 8/3 (2002), 343368.
[MR], [pdf].
M. Drmota, M. Fuchs, and E. Manstavičius.
Functional limit theorems for digital
expansions.
Acta Math. Hungar. 98/3 (2003), 175201.
[MR], [pdf].
M. Fuchs.
On a problem of W. J. LeVeque
concerning metric Diophantine approximation.
Trans. Amer. Math. Soc. 355/5 (2003), 17871801 (electronic).
[MR], [pdf].
W. Steiner.
Generalized de
Bruijn digraphs and the distribution of patterns in
alphaexpansions.
Discrete Math. 263/13 (2003), 247268.
[MR], [pdf].
