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DTSTART:20230312T070000
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DTSTART:20221106T060000
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DTSTART;TZID=America/Toronto:20231031T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-110
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:NICOLO FELLINI\, QUEEN'S UNIVERSITY\n\n\"VARIATIONS OF A CONJE
 CTURE OF ANKENY-ARTIN-CHOWLA\"\n\nA famous conjecture of Ankeny\, Artin an
 d Chowla relates the class\nnumber of a real quadratic field $\\mathbb{Q}(
 \\sqrt{p})$ with $p$ a\nprime congruent to $1\\bmod{4}$\,  with its funda
 mental unit $\\epsilon\n= (t+u\\sqrt{p})/2$ via a $\\bmod{p}$ congruence. 
 In particular\, the\nAnkeny--Artin--Chowla (AAC) conjecture states that $u
 $ is not\ndivisible by $p$. The significance of their conjecture lies in t
 he\nfact that it provides an arithmetic way of computing the class number\
 nof $\\mathbb{Q}(\\sqrt{p})$ for $p$ a prime congruent to $1\\bmod{4}$. I\
 nwill discuss the history and techniques of their work as well as show\nth
 at there are further connections with Fermat quotients and Wieferich\nstyl
 e congruences. This is joint work with M. Ram Murty.\n\nMC 5501
DTSTAMP:20260605T081309Z
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