ON SUMS INVOLVING PRODUCTS AND QUOTIENTS OF L-FUNCTIONS OVER FUNCTION FIELDS

We estimate the sum of products or quotients of L-functions, where the sum is taken over all quadratic extensions of given genus over a fixed global function field. Our estimate for the sum of the quotient of two L-functions is analogous to a result of Schmidt where he estimates the sum of the quotient of two L-series, where the sum is over quadratic extensions of Q with absolute value of the discriminant less than a given bound.