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DTSTART:20240310T070000
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DTSTART:20241103T060000
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UID:69f8ded65ad1c
DTSTART;TZID=America/Toronto:20250129T130000
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TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20250129T140000
URL:https://uwaterloo.ca/pure-mathematics/events/student-number-theory-semi
 nar-73
SUMMARY:Student Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:OWEN SHARPE\, UNIVERSITY OF WATERLOO\n\nThe Selberg-Delange Met
 hod\n\nFor complex w and z\, the expression w^z is ambiguous\, requiring a
 \nchoice of branch of log(w). In particular\, there is no way to make w^z\
 nan entire function of w\; a branch cut will always be present. In turn\,\
 nthis makes it difficult to perform contour integration and calculate\nres
 idues with functions of the form f(w)^z\, which are fundamental\noperation
 s in number theory. We describe Selberg's method for\nperforming such comp
 utations and some of its applications\, such as\nthose by Selberg and Dela
 nge. Incidentally\, we will also discuss\nHankel's formula for the Gamma f
 unction and Perron's formula for\npartial sums of Dirichlet series.\n\nMC 
 5403
DTSTAMP:20260504T180054Z
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