The fourth power moment of automorphic -functions for over a short interval

In this paper we will prove bounds for the fourth power moment in the aspect over a short interval of automorphic -functions for on the central critical line Re. Here is a fixed holomorphic or Maass Hecke eigenform for the modular group , or in certain cases, for the Hecke congruence subgroup with . The short interval is from a large to . The proof is based on an estimate in the proof of subconvexity bounds for Rankin-Selberg -function for Maass forms by Jianya Liu and Yangbo Ye (2002) and Yuk-Kam Lau, Jianya Liu, and Yangbo Ye (2004), which in turn relies on the Kuznetsov formula (1981) and bounds for shifted convolution sums of Fourier coefficients of a cusp form proved by Sarnak (2001) and by Lau, Liu, and Ye (2004).