The paper claims the average fourth moment of holomorphic Hecke cusp forms of weight in [K, K+H], with H = K^(3/4+c), equals 6/pi with a K^(-delta) error, improving Khan's full-length interval result.
On the fourth moment of Hecke-Maass forms and the random wave conjecture
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The fourth moment of holomorphic Hecke cusp forms in shorter intervals
The paper claims the average fourth moment of holomorphic Hecke cusp forms of weight in [K, K+H], with H = K^(3/4+c), equals 6/pi with a K^(-delta) error, improving Khan's full-length interval result.