TITLE: Fourier expansion of Eisenstein Series
QUESTION [7 upvotes]: I have been reading a bit about the Fourier expansion of Eisenstein series (weight 1/2). I came across the fact that the coefficients contain Modified Bessel functions.
Further reading I found articles discussing the zeros of these Bessel functions to behave similar to that of the zeta function (Re(s) = 1/2).
My question, is this or why isn't this a popular way to study Riemann's zeta function? Or have i misunderstood an obvious vital key element?

REPLY [4 votes]: The relationship has actually motivated several studies:

Eisenstein series and the Riemann zeta function (1981) 
Moments of the Riemann zeta function and Eisenstein series part I and part II (2004)  
The Riemann hypothesis for
certain integrals of Eisenstein series (2004)

Some of its limitations are discussed in an answer to this MO question.