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SUMMARY:The distribution of Hecke eigenvalues at Piatetski-Shapiro primes 
 - Stephan Baier (University of Bristol)
DTSTART:20091026T160000Z
DTEND:20091026T170000Z
UID:TALK21041@talks.cam.ac.uk
CONTACT:Boris Bukh
DESCRIPTION:This is joint work with Liangyi Zhao. The distribution of Heck
 e eigenvalues at prime arguments has received a lot of attention. We are i
 nterested in the special question of how they are distributed at arguments
  from a certain sparse set of primes\, namely Piatetski-Shapiro primes.  T
 he motivation for our investigation is two-fold. Firstly\, the mean-values
  of arithmetic functions (in particular\, of Fourier coefficients of cusp 
 forms) over sparse sequences are often difficult to handle and thus of gre
 at interest. Secondly\, it is a hard problem to detect primes in arithmeti
 cally interesting sets of natural numbers that are sparse. To tackle our p
 roblem\, we are using a refinement of a method of Jutila to bound certain 
 exponential sums with Fourier coefficients of cusp forms.
LOCATION:MR12\, CMS
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