zetafunction
Apr17-09, 05:27 PM
i had the following idea but i can not prove if this is right or wrong
let be \sum_{n} a_n exp(-an) \sim f(a)
then \sum _{n \le x}a_{n} \sim g(x)
with the Laplace transform of the derivative g'(x) is equal to f(s=a)
my idea is that if the first condition is true then so is the second.
let be \sum_{n} a_n exp(-an) \sim f(a)
then \sum _{n \le x}a_{n} \sim g(x)
with the Laplace transform of the derivative g'(x) is equal to f(s=a)
my idea is that if the first condition is true then so is the second.