Rest assured that most employers will conduct a reference check if they are seriously considering bringing you on board. But that stage of the hiring process comes well after you submit your resume. For this reason, there’s no need to include “References available upon request” or similar language on the document.
Words make up the vast majority of the content in your resume. But numbers feature prominently too. There’s no way to write a good resume without both. You need numbers to convey your dates of employment, the year you earned a degree or certification, or your requested starting salary range (only if an employer requests that information, though!).