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?

  • 1
    $\begingroup$ Can you explain this connection more clearly? $\endgroup$
    – Kimball
    Jun 13, 2015 at 14:00

1 Answer 1


The relationship has actually motivated several studies:

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

  • $\begingroup$ Your link to Zagier's paper is slightly mangled: it should have mpim-bonn rather than mpimbonn... $\endgroup$ Jun 13, 2015 at 15:24
  • $\begingroup$ I've sen the first link, but not the last two. Thanks I'll check those out. $\endgroup$ Jun 13, 2015 at 17:46

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