628 research outputs found
An abstract Möbius inversion formula with number-theoretic applications
AbstractAn inversion formula for incidence functions is given. This formula is applied to certain types of number-theoretic identities, for example, to the arithmetical evaluation of Ramanujan's sum and to the identical equation of a class of multiplicative functions
A lower bound for the dimension of Bernoulli convolutions
Let and let denote Garsia's entropy for the
Bernoulli convolution associated with . In the present paper
we show that for all and improve this bound
for certain ranges. Combined with recent results by Hochman and
Breuillard-Varj\'u, this yields for all
. In addition, we show that if an algebraic is such that
for some , then
. Such is, for instance, any root of a Pisot number which is
not a Pisot number itself.Comment: 8 pages, no figure
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