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Why exp(pi*sqrt(163)) is almost an integer?

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If you type exp(pi*sqrt(163)) into a normal calculator, it is likely that it will spit out the integer 262,537,412,640,768,744. It turns out, this is not quite right, but you need to go to 12 decimal places to distinguish these two numbers. In this talk, I will discuss the explanation behind this phenomenon, which has its roots in theory of Complex Multipication, a subject which touches on some beautiful ideas in analysis, geometry and number theory.

This talk is part of the The Archimedeans series.

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Via Zoom, and in-person: Large Lecture Theatre, Department of Geography, Downing Site Lecture Room 4, Cambridge University Engineering Department, Trumpington Street, Cambridge CB2 1PZ Mi

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