Joël
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Registered User
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Professor of Mathematics at Brandeis University
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Jun 14 |
accepted | Does every equivalence class of Hecke characters contain a distinguished element? |
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Jun 14 |
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Does every equivalence class of Hecke characters contain a distinguished element? @Kconrad: you're right. $n$ is the degree of $k$ over $\mathbb Q$. I have edited my answer to say this. @Daniel: the map $i$ is canonical. The only freedom you have in defining the isomorphism of $\R$-\algebras $k \otimes_{\mathbb Q} \mathbb R \simeq \mathbb R^{r_1} \times \mathbb C^{r_2}$ is that you can let act the complex conjugacy on each of the $\mathbb C$ factors (hence you have $2^{r_2}$ such isomorphisms). But as far as the embedding of $\R$ is concern, this choice does not change anything. |
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Jun 14 |
revised |
Does every equivalence class of Hecke characters contain a distinguished element? added 148 characters in body |
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Jun 13 |
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Analysis of the boundary of the Mandelbrot set Why the vote to close? The question makes senses. It might have a trivial answer, but I, for one, would be happy to know it... |
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Jun 13 |
answered | Does every equivalence class of Hecke characters contain a distinguished element? |
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Jun 12 |
answered | Independence of an interval and a product set in $\mathbb Z/L\mathbb Z$. |
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Jun 11 |
revised |
Hecke equidistribution edited tags |
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Jun 11 |
awarded | ● Enlightened |
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Jun 11 |
awarded | ● Nice Answer |
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Jun 11 |
awarded | ● Fanatic |
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Jun 11 |
comment |
Heuristic for Montgomery’s conjecture Dear Dimitris, thanks for your answer. Even if it is not exactly what I asked, this is more or less what I needed. Actually, I recently noticed that some non-abelian generalizations of Montgomery's conjecture (suggered by Murty and Murty) are false (I didn't want then to be false, I swear-- I wanted to apply them: but they gave me too strong results to be true). Now I am trying to understand what goes wrong, in order to get a conjecture that might be correct. I will try to work out what this heuristics give in the non-abelian case, and see what comes out. |
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Jun 11 |
revised |
Extensions of Galois representations typos corrected |
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Jun 11 |
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Independence of an interval and a product set in $\mathbb Z/L\mathbb Z$. Interesting. So my question would be a dynamical system question, kind of... But I don't understand what you mean by: "use Cauchy-Schwarz inequality to complete the variable" |
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Jun 10 |
answered | Why is it a good idea to study a ring by studying its modules? |
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Jun 10 |
asked | Independence of an interval and a product set in $\mathbb Z/L\mathbb Z$. |
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Jun 10 |
revised |
Extensions of Galois representations deleted 286 characters in body |
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Jun 10 |
revised |
Extensions of Galois representations added 320 characters in body |
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Jun 10 |
accepted | Extensions of Galois representations |
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Jun 10 |
revised |
Extensions of Galois representations added 456 characters in body; added 7 characters in body; added 63 characters in body |
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Jun 10 |
revised |
Extensions of Galois representations edited tags |
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Jun 10 |
answered | Extensions of Galois representations |
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Jun 9 |
accepted | Galois deformations with Panchiskin condition |
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Jun 8 |
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What is the source of this famous Grothendieck quote? This is an interesting quote. Yet the idea that definitions are the most important "vehicles" of mathematical rigor is very old, and has been perfectly expressed already by Pascal in "l'art de persuader". A more original idea is the one of Grothendieck, that definition may have an even higher role in mathematics, as vehicle not only of rigor, but of mathematical creativity itself. That is, the creative work of a mathematicians is not mainly to prove good theorems, it is to "invent" good definitions. His works are a sufficient illustration of this new maxim. |
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Jun 8 |
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What is the source of this famous Grothendieck quote? For what it's worth: I have read "récoltes et semailles" years ago, but this quote doesn't ring any bell. – Joël 0 secs ago |
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Jun 8 |
revised |
Primes in short intervals with a preassigned frobenius added 1353 characters in body |
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Jun 7 |
revised |
Primes in short intervals with a preassigned frobenius deleted 1305 characters in body |
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Jun 7 |
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Primes in short intervals with a preassigned frobenius You're both right. I will reformulate my question... |
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Jun 7 |
revised |
Primes in short intervals with a preassigned frobenius edited tags |
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Jun 7 |
answered | Roadmap to reach Arithmetic Geometry for a Physics Major |
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Jun 7 |
asked | Primes in short intervals with a preassigned frobenius |
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Jun 7 |
awarded | ● Citizen Patrol |
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Jun 7 |
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Principal series of finite group of Lie type Thanks for giving these details. |
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Jun 7 |
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Principal series of finite group of Lie type Thanks to all three of you, Matt, Jim and Jay. After a crash self-course on Deligne-Luztig theory (how beautiful!), I now understand your arguments, which are basically the same. |
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Jun 6 |
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Principal series of finite group of Lie type I stay tuned. Thanks already. |
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Jun 6 |
revised |
Principal series of finite group of Lie type added 1 characters in body |
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Jun 6 |
asked | Principal series of finite group of Lie type |
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Jun 5 |
asked | Heuristic for Montgomery’s conjecture |
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Jun 5 |
awarded | ● Nice Answer |
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Jun 5 |
answered | Modular symbols and degeneracy maps |
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Jun 5 |
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Modular symbols and degeneracy maps You're asking if the Ihara's lemma is true in the context of modular symbols... |
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Jun 3 |
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Is Gouvêa-Mazur’s “Infinite Fern” a fractal? I think the question is interesting, but somehow is still not well-posed. There is the problem of what is a fractal, discussed in earlier comments, but also the problem of what is the "infinite fern". I mean, it is a rigid analytic varieties, but there are at least three ways to formalize this notion, Tate's and Berkovich's and Huber's. Each leads to a different space.. |
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Jun 1 |
accepted | Examples of (Phi,Gamma)-modules |
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May 31 |
answered | Effective Chebotarev without Artin’s conjecture |
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May 30 |
revised |
Examples of (Phi,Gamma)-modules added 1213 characters in body |
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May 30 |
answered | Galois deformations with Panchiskin condition |
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May 29 |
answered | Examples of (Phi,Gamma)-modules |
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May 29 |
answered | etale cohomology of an abelian variety and its dual |
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May 28 |
accepted | Would a proof of Ramanujan Conjecture together with other known results about automorphic L-functions imply the Grand Riemann Hypothesis? |
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May 28 |
answered | Would a proof of Ramanujan Conjecture together with other known results about automorphic L-functions imply the Grand Riemann Hypothesis? |
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May 25 |
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Effective Chebotarev without Artin’s conjecture Dear Frank: yes, I have been playing with that circle of ideas since a while. IK state without ambiguity that the strong formula (the one which implies an error term in square root of the size of the conjugacy set) holds with just GRH, without Artin. They may have meant otherwise but this is what they write. I have started a bounty to give this question more visibility, hoping that someone would help us resolve this situation: a strong result appearing in the (main stream) literature but for which no proof is to be found. |
