Mean Calculation Of Divisors And Functions On Square-free Polynomials Over Function Fields And Its Applicatio

How to estimate the average of number theory function constitutes a significant problem in analytic number theory and its findings are important basis for solving other problems of analytic number theory.In this paper,we have studied two problems: the first one is about the mean value of divisor sum function at the set of square-free polynomials in function fields;the second one is about the sum of the maximum values of two divisor functions in function fields.For the first problem,we obtain its asymptotic value through the methods of Riemann zetafunction,the Euler product of the Dirichlet series,Laurent theorem and so on.With regard to the second problem,we acquire its asymptotic value by the method of Euler product used on the first problem.Below is the structure of this paper.In the first chapter,we will introduce the research background and the main results.In the second chapter,we will recommend the fundamental knowledge which is required for this paper.In the third chapter,we will calculate the average of divisor sum function at the set of square-free polynomials in function fields and acquire an asymptotic value.In the fourth chapter,we will estimate the sum of the maximum values of two divisor functions by the method which have appeared in the third chapter.