A note on the global Langlands conjecture.
We generalize Poor and Yuen’s inequality to the Hermite–Rankin constant and the Bergé–Martinet constant . Moreover, we determine explicit values of some low- dimensional Hermite–Rankin and Bergé–Martinet constants by applying Rankin’s inequality and some inequalities proven by Bergé and Martinet to explicit values of , and ().
The main purpose of this paper is to use the analytic method to study the calculating problem of the general Kloosterman sums, and give an exact calculating formula for it.