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SUMMARY:Liem Nguyen (Louisiana State University)
DTSTART:20210119T203000Z
DTEND:20210119T210000Z
DTSTAMP:20260423T021218Z
UID:POINT/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/24/">O
 n the Values and Spectrum of Weil Sum of Binomials</a>\nby Liem Nguyen (Lo
 uisiana State University) as part of POINT: New Developments in Number The
 ory\n\n\nAbstract\nThe Weil sum of an additive character $\\mu$ over a fin
 ite field $F$ is defined to be $W_{F\,s}(a)=\\sum_{x \\in F} \\mu(x^s-ax)$
  where $s$ is an integer coprime to $|F^*|$. The Weil spectrum counts dist
 inct values of the Weil sum as $a$ runs through the invertible elements in
  the finite field. Determining the values of these sums and the size of it
 s spectrum give answers to long-standing problems in cryptography\, coding
  and information theory. In this talk\, we prove a special case of the Van
 ishing Conjecture of Helleseth ($1971$) on the presence of zero in the Wei
 l spectrum. We then propose a new conjecture on when the Weil spectrum con
 tains at least five elements\, and prove it for a certain class of Weil su
 m.\n\nTo join the talks on January 19th\, please register here:  \n\nhttps
 ://ucsd.zoom.us/meeting/register/tJIuf-6uqjoiH9eVbtLN9y1G9l0qEBmbDRmV\n
LOCATION:https://researchseminars.org/talk/POINT/24/
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