We develop an approach to study character sums, weighted by a multiplicative function $f:\mathbb{F}_q[t]\to S^1$, of the form \begin{equation} \sum_{G\in \mathcal{M}_N}f(G)\chi(G)\xi(G), \end{equation} where $\chi$ is Dirichlet and $\xi$ short interval over $\mathbb{F}_q[t].$ then deduce versions Matom\"aki-Radziwill theorem Tao's two-point logarithmic Elliott conjecture fields $\mathbb{F}_q[t]...

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

there are several kinds of hyperrings, for example, krasnerhyperrings, multiplicative hyperring, general hyperrings and$h_v$-rings. in a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. in this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf keywords:} multiplic...

Let K be a field of characteristic 0, f : N → K be a multiplicative function, and F (z) = P n≥1 f (n)z n ∈ K[[z]] be algebraic over K(z). Then either there is a natural number k and a periodic multiplicative function χ(n) such that f (n) = n k χ(n) for all n, or f (n) is eventually zero. In particular , the generating function of a multiplicative function f : N → K is either transcendental or r...

We note how several central results in multiplicative number theory may be rephrased naturally in terms of multiplicative functions f that pretend to be another multiplicative function g. We formalize a ‘distance’ which gives a measure of such pretentiousness, and as one consequence obtain a curious inequality for the zeta-function. A common theme in several problems in multiplicative number th...