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SUMMARY:Maksym Radziwill (Caltech)
DTSTART:20211014T213000Z
DTEND:20211014T223000Z
DTSTAMP:20260423T005828Z
UID:JNTS/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JNTS/25/">Bi
 as in cubic Gauss sums</a>\nby Maksym Radziwill (Caltech) as part of Colum
 bia CUNY NYU number theory seminar\n\n\nAbstract\nI will discuss recent wo
 rk with Alex Dunn. Conditionally on the Generalized Riemann Hypothesis we 
 establish a conjecture of S. Patterson from 1978 concerning the existence 
 of a bias in cubic Gauss sums. This explains a well-known numerical bias f
 irst observed by Kummer in 1846. The proof relies on the use of metaplecti
 c forms for the cubic cover of $GL_2$ and on a new ”dispersion” estima
 te for cubic Gauss sums. Along the way we show that the cubic large sieve 
 of Heath-Brown is sharp\, contrary to widely held expectations. I will exp
 lain the tools alluded to above\, the rationale for the tools and the main
  moments of the proof.\n
LOCATION:https://researchseminars.org/talk/JNTS/25/
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