Multiplicative functions additive on polygonal numbers
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DOI: 10.1007/s00010-021-00824-8
Abstract: We prove that the set $$\mathcal {P}$$ ( $$\mathcal {H}$$ , resp.) of all positive pentagonal (hexagonal, resp.) numbers is an additive uniqueness set for the collection of multiplicative functions; if a multiplicative function f… read more here.
Keywords: polygonal numbers; additive polygonal; resp; multiplicative functions ... See more keywords
Multiplicative functions additive on generalized pentagonal numbers
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DOI: 10.1016/j.crma.2017.12.011
Abstract: Abstract We prove that the set GP of all nonzero generalized pentagonal numbers is an additive uniqueness set; if a multiplicative function f satisfies the equation f ( a + b ) = f (… read more here.
Keywords: additive generalized; generalized pentagonal; pentagonal numbers; multiplicative functions ... See more keywords
A note on multiplicative automatic sequences
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DOI: 10.1016/j.crma.2019.10.002
Abstract: Abstract We prove that any q-automatic completely multiplicative function f : N → C essentially coincides with a Dirichlet character. This answers a question of J.-P. Allouche and L. Goldmakher and confirms a conjecture of… read more here.
Keywords: automatic sequences; multiplicative automatic; multiplicative functions; completely multiplicative ... See more keywords
Correlations of multiplicative functions and applications
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DOI: 10.1112/s0010437x17007163
Abstract: We give an asymptotic formula for correlations $$\begin{eqnarray}\mathop{\sum }_{n\leqslant x}f_{1}(P_{1}(n))f_{2}(P_{2}(n))\cdots f_{m}(P_{m}(n)),\end{eqnarray}$$ where $f,\ldots ,f_{m}$ are bounded ‘pretentious’ multiplicative functions, under certain natural hypotheses. We then deduce several desirable consequences. First, we characterize all multiplicative functions… read more here.
Keywords: multiplicative functions; functions applications; correlations multiplicative;