Go to Karthus advanced build 900 ap.

Oh really? buy 6 archangels so you will have 1150 + ap or 5 if you like 900 :) and boots of sorc.

I perfer 3 zhonyahs, boots, arch's and either abyssal scepter or void staff, depending on which I need more. And if the game is sitll going, then I sell void staff and get another arch's or zhonyahs, if I need the ap asap then I go zhonyahs but if we're still pushing and I've got the time to power up arch's then I'll will take my time to do it.

zonyas ring isn;t better AP providing then archangel's staff. If u get 4k mana (easily possible with karthus) it's a 100AP bonus with archangel's staff, together 145AP, and the 25%bonus with zonyas is unique so you only need one ring...

i once got so many kills that i had 6 z rings which made karthus godly, and i built archangel, z ring, sorc boots, soulstealer, and i think voidstaff but got so many kills i had 945+ ab ult was crazy

Since you aren't going for wall of pain you should get Rylai's Crystal Scepter as a must have item rather than two Zhonya's Ring which do not stack