Weil Conjectures - Applications

Applications

• Deligne (1980) was able to prove the hard Lefschetz theorem (part of Grothendieck's standard conjectures) using his second proof of the Weil conjectures.
• Deligne (1971) had previously shown that the Ramanujan-Petersson conjecture follows from the Weil conjectures.
• Deligne (1974, section 8) used the Weil conjectures to prove estimates for exponential sums.