The amount of beakers, gold, or culture from building Research, Wealth and Culture is equal to half the city's production fed through production modifiers (NOT research, gold, or culture modifiers, so your Libraries, Banks, and Pavilions WON'T have an effect, while your Forges WILL).
Research building (RB) is enabled by Alphabet; use RB to tech to the more efficient (explained later) Current, while allows you to build wealth (WB); WB will allow you to raise your tech slider, increasing research output across the empire instead of in just one city (as RB does). Also, I suggest using WB either pre-beeline (to stock up gold for a 100% research rush) or post-military-tech-acquisition, since you can use stockpiled gold to insta-upgrade your Axemen into Riflemen. I don't have much experience with Culture building, but the AIs like to use it on late game new cities (either settled or conquered), and it's probably helpful for a culture win.