Overpartitions and functions from multiplicative number theory

Publication date: 2 February 2021

Abstract: Let

a l p h a

and

be two nonnegative integers such that

. For an arbitrary sequence

{a_{n}}_{n g e q s l a n t 1}

of complex numbers, we consider the generalized Lambert series in order to investigate linear combinations of the form

, where

S (k, n)

is the total number of non-overlined parts equal to

k

in all the overpartitions of

n

. The general nature of the numbers

a_{n}

allows us to provide connections between overpartitions and functions from multiplicative number theory.

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