67 research outputs found
High moments of the Riemann zeta-function
The authors describe a general approach which, in principal, should produce
the correct (conjectural) formula for every even integer moment of the Riemann
zeta function. They carry it out for the sixth and eigth powers; in the case of
sixth powers this leads to the formula conjectured by Conrey and Ghosh, and in
the case of eighth powers is new.Comment: Abstract added in migratio
Remarks on a Formula of Ramanujan
Assuming an averaged form of Mertens' conjecture and that the ordinates of
the non-trivial zeros of the Riemann zeta function are linearly independent
over the rationals, we analyze the finer structure of the terms in a well-known
formula of Ramanujan
Universality of -Functions over function fields
We prove that the Dirichlet -functions associated with Dirichlet
characters in are universal. That is, given a modulus of
high enough degree, -functions with characters to this modulus can be found
that approximate any given nonvanishing analytic function arbitrarily closely.Comment: 18 pages. Comments are welcome
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