Divyum Sharma, Department of Pure Mathematics, University of Waterloo
"Joint distribution of the base-q and Ostrowski digital sums"
In
1922,
A.
Ostrowski
introduced
a
numeration
system
based
on
the denominators
of
the
convergents
in
the
continued
fraction expansion
of
a
fixed
irrational
number
\alpha.
Coquet,
Rhin
and Toffin
studied
the
joint
distribution
in
residue
classes
of
the base-q sum-of-digits
function
Sq and
the
Ostrowski sum-of-digits
function
S_\alpha.
They
gave
certain
sufficient conditions
for
the
set
{n\in\mathbb{N}:
S_{q}(n)\equiv
a_1\pmod{m_1},\
S_{\alpha}(n)\equiv a_2\pmod{m_2}\}
to
have
asymptotic
density
1/m1m2. In
this
talk,
we
present
a quantitative
version
of
their
result
when
\alpha=[0;\overline{1,m}],\
m\geq
2.
MC 5501