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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240328T130000
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URL:https://uwaterloo.ca/pure-mathematics/events/student-number-theory-semi
 nar-66
SUMMARY:Student Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:TALK #1: TED FU\, UNIVERSITY OF WATERLOO\n\n\"ON WARING'S PROBL
 EM FOR LARGE POWERS\"\n\nLet G(k) be the least number _s_ having the prope
 rty that every\nsufficiently large natural number is the sum of at most _
 s_ positive\ninteger _k_-th powers. In this talk\, I will present how Brü
 dern and\nWooley implement smooth numbers technologies in their minor arc\
 nanalysis and derive G(k) ≤ ⌈k(log k + 4.20032)⌉.\n\nTALK #2: AIDAN
  BOYLE\, UNIVERSITY OF WATERLOO\n\n\"WARING’S PROBLEM: BEYOND FREIMAN’
 S THEOREM\"\n\nSuppose that we are given a non-decreasing sequence of posi
 tive\nintegers (ki) where each term is at least 2. Given a positive intege
 r\nj\, we seek to understand the circumstances in which there exists a\npo
 sitive integer s := s(j) such that every sufficiently large natural\nnumbe
 r n can be written as a sum of s positive integers to the\nrespective powe
 rs kj\, ...\, kj+s-1. Freĭman asserted that such\nrepresentation exists i
 f and only if the infinite summation of all\n1/ki diverges. We provide an 
 effective version of this theorem\, and in\nparticular\, comment on instan
 ces in which the exponents form a\nsequence of consecutive terms of an ari
 thmetic progression.\n\nMC 5417
DTSTAMP:20260506T210829Z
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