Abstract

Recently Blomer showed that if α ( n ) denote the normalized Fourier coefficients of any holomorphic cusp form f with integral weight, then ∑ b = 1 q | ∑ n ⩽ X n ≡ b ( mod q ) α ( n ) | 2 ≪ f , ε X 1 + ε holds uniformly in q ⩽ X . By an elementary argument we show that independent of q, ∑ b = 1 q | ∑ n ⩽ X n ≡ b ( mod q ) α ( n ) | 2 ≪ f X ( log X ) 2 , where α ( n ) could be the normalized Fourier coefficients of any reasonable cusp forms, including Maass cusp forms, holomorphic cusp forms with half-integral or integral weights.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call