1. Larry Niven: Niven wrote a lot of excellent "hard" science fiction in the '70s and '80s. Some of it has been OTBE'd (Overtaken By Events) but it's still fun.
A. He invented the term "Belter."
B. He came up with the "Belter crest" - a high Mohawk to which The Expanse pays tribute with the topknot fades of Naomi Nagata and Detective Miller.
D. Niven also invented "Confinement Asteroid" - a place where Belter kids could grow up in relatively high gravity to avoid the "long bone" syndrome we see in the series.
2. Robert Heinlein: A writer who probably needs no introduction.
A. At one point, Holden's navigator and lover Nygard talks about the Knight shuttle flying "teakettle" to the Scopuli. Teakettle is a term Heinlein invented to distinguish notional fission-propulsion rockets from more powerful ships powered by fusion and direct matter conversion ("torch ships"). Atomic ships were "teakettles" because their fission piles heated water or other reaction mass to boiling and shot them out the back for propulsion.
B. The Ceres Belter Creole may also be a nod to the patois spoken by Heinlein's characters in his famous (or notorious) novel The Moon Is A Harsh Mistress. Those characters, not coincidentally, face the same political situation as the Ceres residents: They can never go back to Earth, and Earth forces them to provide vital resources and pays them nothing in return.
3. Isaac Asimov: Asimov was one of the first to write about mining the Saturn system for water ice in his story The Martian Way. Holden's original ship, the ice-hauler Canterbury, owes Prof. Isaac a nod. The Martian Way also deals with the some of the same questions of interplanetary economics as The Expanse - the intersection of nationalism and resource-scarcity economics - and outlined the growing sense of a new Mars-based patriotism. These are all themes you'll encounter in The Expanse.
Update: You could call most of these things "homage," but maybe a more accurate term is "prior art." Certain ideas - like the Saturnian ice - are obvious conclusions from existing situations. Referring to them when writing about interplanetary (as opposed to interstellar) travel is just building on the foundations laid beforehand by folks like Clarke, Asimov, and Heinlein.