Short-interval averages of sums of Fourier coefficients of cusp forms

Chandrasekharan and Narasimhan [2] showed that the Classical Conjecture for Sf(X) holds on average over intervals of length X. Jutila [10] improved this result to show that the Classical Conjecture for Sf(X) holds on average over short intervals of length X34+ϵ. Building on the results and analytic information about ∑|Sf(n)|2n−(s+k−1) from our recent work [9], we further improve these results to show that the Classical Conjecture for Sf(X) holds on average over short intervals of length X23(log⁡X)16.