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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20250212T130000
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URL:https://uwaterloo.ca/pure-mathematics/events/student-number-theory-semi
 nar-75
SUMMARY:Student Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:ADAM JELINSKY\, UNIVERSITY OF WATERLOO \n\nThe Completing Techn
 ique for sums of periodic complex valued functions\n\nIn Iwaniec and Kowal
 ski's book on analytic number theory\, they detail\nwhat they call the \"c
 ompleting technique\" to evaluate bounds on\nincomplete sums of periodic f
 unctions Z^n->C by \"completing\" it by\nfinding an equivalent complete su
 m over all Z/qZ. In this talk we will\ndiscuss how this completion techniq
 ue can be used to prove the\nPolya-Vinogradov inequality\, which gives a n
 early tight bound on all\nsums of Dirichlet characters over the interval [
 N\,N+M]. From this we\nwill discuss other applications of this method\, an
 d give examples\nwhere this method fails to give a bound that is nontrivia
 l. \n\nMC 5403
DTSTAMP:20260504T180042Z
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