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SUMMARY:Ken Ono (University of Virginia)
DTSTART:20200907T140000Z
DTEND:20200907T150000Z
DTSTAMP:20260423T052710Z
UID:EIMINT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EIMINT/1/">V
 ariations of Lehmer’s Conjecture on the Nonvanishing of the Ramanujan ta
 u-function</a>\nby Ken Ono (University of Virginia) as part of EIMI Number
  Theory Seminar\n\n\nAbstract\nIn the spirit of Lehmer's unresolved specul
 ation on the nonvanishing of Ramanujan's tau-function\, it is natural to a
 sk whether a fixed integer is a value of $\\tau(n)$\, or is a Fourier coef
 ficient of any given newform.  In joint work with J. Balakrishnan\, W. Cra
 ig\, and W.-L. Tsai\, the speaker has obtained some results that will be d
 escribed here. For example\, infinitely many spaces are presented for whic
 h the primes $\\ell\\leqslant 37$ are not absolute values of coefficients 
 of any new forms with integer coefficients. For Ramanujan’s tau-function
 \, such results imply\, for $n>1$\, that $\\tau(n)\\notin \\{\\pm \\ell\\\
 ,:\\\, \\ell<100\n\\\,\\text{is odd prime}\\}$.\n
LOCATION:https://researchseminars.org/talk/EIMINT/1/
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