The first chapter should include the following points:- 1

The first chapter should include the following points:- 1. complex manifold 2. holomorphic line bundle 3. bergman kernel Bk (X) 4. How Bergman kernel is related to holomorphic line bundle. 5. Estimates of Bergman kernel. 6. Invidual estimates of cusp form is same as estimate of bergman kernel Bk Γ i.e, {f1, ..., fdk } be the orthonormal basis , then bergman kernel is defined as sum dk i=1|fi | 2 = Bk Γ will have the estimate OX(k n) and the individual cusp forms will have the similar estimate |fi | = OX(k n).