The multi-classing rules subsection on spell slots says:
Spell Slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, and half your levels (rounded down) in the paladin and ranger classes. Use this total to determine your spell slots by consulting the Multiclass Spellcaster table.
Does this mean that a Eldritch Knight fighter 3/Arcane Trickster rogue 3 has 0 spell slots?
Both of these classes use the Wizard spell list, if that makes a difference.
I am not asking if multiclassed spellcasters share spell slots; I am asking based on the basic rules how they are calculated for these specific classes. Where do the rules address multiclass spellcasting involving the Eldritch Knight fighter or Arcane Trickster rogue?
Best Answer
One third of the levels of each
In the multiclass spellcasting rules in the Player's Handbook (page 164), the Arcane Trickster and Eldritch Knight are mentioned as counting one third of their levels in Rogue and Fighter, rounded down.
An Arcane Trickster 3/Eldritch Knight 3 would have spell slots as 2nd level on the Multiclass Spellcaster table, which is 3 1st-level slots.
The reason you didn't find them in the link you provided is because the basic rules/SRD don't include the Arcane Trickster rogue subclass or Eldritch Knight fighter subclass, which is why the multiclass spellcasting rules there don't account for those 2 subclasses.