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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240312T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-117
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:AMIR AKBARY\, UNIVERSITY OF LETHBRIDGE\n\n\"ETA-QUOTIENTS WHOSE
  DERIVATIVES ARE ETA-QUOTIENTS\"\n\nThe Dedekind eta function is defined b
 y the infinite product\n\\[\n\\eta(z) = e^{\\pi i z/12}\\prod_{n=1}^\\inft
 y (1 - e^{2 \\pi i z}) =\nq^{1/24}\\prod_{n=1}^\\infty (1 - q^n).\n\\]\nan
 d\n\\[\nf(z) = \\prod_{t\\mid N} \\eta^{r_t}(tz)\,\n\\]\nwhere the exponen
 t r_t are integers. Let k be an even positive\ninteger\, p be a prime\, an
 d m be a nonnegative integer. We find an\nupper bound for orders of zeros 
 (at cusps) of a linear combination of\nclassical Eisenstein series of weig
 ht k and level p^m. As an immediate\nconsequence\, we find the set of all 
 eta quotients that are linear\ncombinations of these Eisenstein series and
 \, hence\, the set of all eta\nquotients of level p^m whose derivatives ar
 e also eta quotients.\n\nThis is joint work with Zafer Selcuk Aygin (North
 western Polytechnic).\n\nMC 5417
DTSTAMP:20260506T220736Z
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