2.1 To find an asymptotic formula for the eighth moment of families of degree 2 L-functions associated with holomorphic modular forms. In particular, we want to compute the main term and bound the error terms for T_4(q), the eighth moment of a family of L-functions associated with Gamma_1(q) and short average over t. 2.2 To develop new techniques to study properties of L-functions. We expect the eighth moment T_4(q) to be more difficult to compute than the sixth moment T_3(q).
2.3 To rearrange the main term and compare it with a conjecture of the eighth moment of L-functions of degree 2.
2.5 If time permits, we will study another family of the eighth moment B_4(q) of a family of L-functions associated with Gamma_1(q) without a short average over T and find an unconditional bound for it.
