633 research outputs found
Knot points of typical continuous functions
It is well known that most continuous functions are nowhere differentiable.
Furthermore, in terms of Dini derivatives, most continuous functions are
nondifferentiable in the strongest possible sense except in a small set of
points. In this paper, we completely characterise families S of sets of points
for which most continuous functions have the property that such small set of
points belongs to S. The proof uses a topological zero-one law and the
Banach-Mazur game.Comment: 24 page
The Bowman-Bradley theorem for multiple zeta-star values
The Bowman-Bradley theorem asserts that the multiple zeta values at the
sequences obtained by inserting a fixed number of twos between 3,1,...,3,1 add
up to a rational multiple of a power of pi. We establish its counterpart for
multiple zeta-star values by showing an identity in a non-commutative
polynomial algebra introduced by Hoffman.Comment: 17 page
Analogues of the Aoki-Ohno and Le-Murakami relations for finite multiple zeta values
We establish finite analogues of the identities known as the Aoki-Ohno
relation and the Le-Murakami relation in the theory of multiple zeta values. We
use an explicit form of a generating series given by Aoki and Ohno.Comment: 6 page
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