On the mean value of the functions related to the divisor function on the ring of polynomials over a finite field

zbMATH Open1470.11315arXiv1907.05105MaRDI QIDQ5154434

Author name not available (Why is that?)

Publication date: 5 October 2021

Abstract: Let

m a t h b b F_{q} [T]

, be the ring of polynomials over a finite field

m a t h b b F_{q}

. Let

g : m a t h b b F_{q} [T] i g h t a r r o w m a t h b b R

be a multiplicative function such that for any irreducible polynomial

P

over

m a t h b b F_{q}

and any

k g e 1

, the equality

d_{k} = g (P^{k})

holds for some arbitrary sequence of reals

{d_{k}}_{k = 1}^{i n f t y}

. In this paper, we get an explicit formula for the sum

T (N) = sumlimits_{substack{deg F=N F ext{ is monic}}}{g (F)},

and also derive different asymptotics when this sum in cases of

q o i n f t y; q o i n f t y, N o i n f t y; q^{N} o i n f t y

.

Full work available at URL: https://arxiv.org/abs/1907.05105

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