Convex Holder bound and its applications

TL;DR

This paper introduces a convex Holder bound that relates different norms and demonstrates its applications in bounding functions like the zeta function, binomial sums, and gamma and beta functions.

Contribution

It presents a new convex Holder bound that connects l, s, and m norms, with novel applications in bounding special mathematical functions.

Findings

Derived an upper bound on the s norm using l and m norms.

Applied the bound to estimate the zeta function and binomial sums.

Extended the bound to gamma and beta functions.

Abstract

Given l<s<m an upper bound on the s norm is given using l norm and m norm. The result is applied in bounding odd values of zeta function, binomial sums and gamma and beta functions.