Let $\mathbb{F}_q(T)$ be the field of rational functions in one variable over a finite field. We introduce notion totally $T$-adic function: that is algebraic and whose minimal polynomial splits completely completion $\mathbb{F}_q(\!(T)\!)$. give two proofs height nonconstant function bounded away from zero, each which provides sharp lower bound. spend majority paper providing explicit construc...

The main purpose of this paper is to deal with the uniqueness of meromorphic functions sharing sets concerning small functions. We obtain two main theorems which improve and extend strongly some results due to R. Nevanlinna, Li-Qiao, Yao, Yi, Thai-Tan, and Cao-Yi.

Motivated by recent results, we study sums of the formSf(x)=∑n≤xf(⌊xn⌋), where f is an arithmetic function and ⌊⋅⌋ denotes greatest integer function. We improve error term in asymptotic formula for Sf(x) some specific cases.