Timeline for Gauss linking integral and quadratic reciprocity
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 23, 2013 at 19:04 | comment | added | Cam McLeman | Fair enough, I concede the point. Sorry! | |
| Sep 23, 2013 at 18:56 | comment | added | John Pardon | I want a closer relationship between gauss sums and the U(1) path integral which reduces to the gauss linking number integral. Obviously I want more than just saying "both look roughly like $\int_{\mathbb R}e^{-x^2}\,dx$". The answer you wrote is a great exposition of the analogy between Legendre symbols and linking numbers, but you haven't said anything about my actual question. | |
| Sep 23, 2013 at 18:40 | comment | added | Cam McLeman | Well, the Gaussian sums are pretty clearly a discrete analog of the Gaussian integrals, right? And so Gauss sums give Legendre symbols like Gaussian integrals give linking numbers. Unless I'm misunderstanding, it sounds like your question may be more on the gauge-theoretic side (why Gaussian integrals are related to Gauss's linking number formula) than anything to do with arithmetic topology. | |
| Sep 23, 2013 at 18:09 | comment | added | John Pardon | But how do Gauss sums fit into this picture? (that's really what my question is about). | |
| Sep 23, 2013 at 17:33 | history | edited | Cam McLeman | CC BY-SA 3.0 |
added 95 characters in body
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| Sep 23, 2013 at 17:26 | comment | added | Cam McLeman | Apologies in advance for subscript/superscript and $p$ vs. $q$ issues which undoubtedly permeate this response. | |
| Sep 23, 2013 at 17:25 | history | answered | Cam McLeman | CC BY-SA 3.0 |