Abstract
The main part of this thesis aims at establishing the functional equa- tion of Rankin L-functions over arbitrary global function fields k with odd characteristic. Fixing an " infinite" place ∞ of k, we consider an imaginary quadratic field extension K/k (meaning ∞ does not split in K/k). Func- tional equation is proved for Rankin L-function formed by an automorphic cusp forms of Drinfeld type together with a theta function associated with given ideal class group character of K/k. This work generalizes previous results obtained by Rück-Tipp (functional equation over the rational func- tion fields ). We also derive a Wiener-Ikehara Tauberian theorem for global function fields in the last chapter for use in the analytic problems concerning arithmetic statistics. Asymptotic formulas for counting positive divisors of a given function field is investigated. This allows us to get in particular an asymptotic formula for the proportion of polynomials of a given degree over a finite field which do not have odd degree irreducible factors.