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# Aleksandar Bahat

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 Name Aleksandar Bahat Member for 10 months Seen May 24 at 17:18 Website Location New Orleans, LA Age
 Mar16 revised Where was the arithmetic zeta function of a scheme first defined?Changed tags Mar16 asked Where was the arithmetic zeta function of a scheme first defined? Mar11 awarded ● Good Answer Feb22 awarded ● Fanatic Feb14 awarded ● Civic Duty Feb8 awarded ● Autobiographer Feb7 comment What do theta functions have to do with quadratic reciprocity?Correction: that should read "generating functions" rather than "generated functions". Feb7 awarded ● Critic Feb6 comment Algebraic number theory: building and simplifyingThe problem is, however, that schemes and cohomology could just as well fall under the "building new things" category... Feb6 comment Algebraic number theory: building and simplifyingI'm not sure if this counts as a "simplification" per se (which is why I'm posting it as a comment), but certainly arithmetic geometry can make some number theoretic results more "natural", at least for someone like me who likes to think geometrically. Although schemes and cohomology may not fit your criterion of accessibility to undergraduates, they could rightfully be considered a means of simplifying parts of algebraic number theory. Feb6 awarded ● Commentator Feb4 awarded ● Scholar Feb2 comment fourier analytic proofsI believe the first appearance of this proof is in the paper "Uber die Gausschen Summen" by Issai Schur. Jan31 comment What do theta functions have to do with quadratic reciprocity?I suspected there was something Langlands-y about this. That's probably the best "big picture" explanation. Unfortunately, I don't know enough about Langlands to get very far with this. I like what you're getting at in the last paragraph; Jacobi's proof is "natural" (in the sense that generated functions are natural), and so I guess it's not a big leap to try to generalize that. Jan31 comment What do theta functions have to do with quadratic reciprocity?I've heard of Hecke's generalization before, but I still feel my "Why should we expect..." question is unresolved. Although the usefulness of analytic functions in number theory is no longer surprising to me, I'd like to understand specifically why somebody would see quadratic reciprocity and think, "Hmm, $\theta(z)=z^{-1/2}\theta(1/z)$ is relevant." Why this piece of analysis in particular? Jan28 comment What do theta functions have to do with quadratic reciprocity?Interesting! I didn't know about Dedekind sums. I'll have to read up on this some time soon. Yet another piece of the grand puzzle... Jan28 awarded ● Nice Question Jan28 asked What do theta functions have to do with quadratic reciprocity? Jan5 comment Can we categorify the formula for the quadratic Gauss sum?Thanks for your comment. I've heard of that result before somewhere, but never managed to track down a reference. It's very interesting, but doesn't really answer my question. If I had some result about objects that decategorified to this Gauss sum identity, then this paper might give me a proof "for free"; the problem is, I don't know what to prove about the objects yet! Jan3 awarded ● Student Jan3 asked Can we categorify the formula for the quadratic Gauss sum? Jan3 awarded ● Nice Answer Jan2 comment New grand projects in contemporary mathAlso, thank you for pointing that out from the paper. There is definitely still a long way to go before we "really find" $\mathbb{F}_1$, but from what I know, this is one of the most substantial theoretical developments so far. Jan2 comment New grand projects in contemporary mathWell, if Durov's definition solved the Riemann hypothesis, I think we would have heard! Jan2 answered New grand projects in contemporary math