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DTSTART;TZID=America/Los_Angeles:20230425T121500
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DTSTAMP:20260419T182510
CREATED:20230116T180753Z
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UID:3027-1682424900-1682428200@colleges.claremont.edu
SUMMARY:Bias in cubic Gauss sums: Patterson's conjecture (Alex Dunn\, CalTech)
DESCRIPTION:We prove\, in this joint work with Maksym Radziwill\, a 1978 conjecture of S. Patterson (conditional on the Generalized Riemann Hypothesis) concerning the bias of cubic Gauss sums. This explains a well-known numerical bias in the distribution of cubic Gauss sums first observed by Kummer in 1846. One important byproduct of our proof is that we show Heath-Brown’s cubic large sieve is sharp under GRH.  This disproves the popular belief that the cubic large sieve can be improved. An important ingredient in our proof is a dispersion estimate for cubic Gauss sums. It can be interpreted as a cubic large sieve with correction by a non-trivial asymptotic main term.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-alex-dunn-caltech/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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