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Professor of Mathematics at Brandeis University


Apr
9
comment Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$
Je vais le faire.
Apr
9
comment Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$
@Aurel, But I am very happy to have heard about this paper by Winckler. I wonder if he can also find values for the constants in the effective version of Chebotarev that you get assuming not only GRH, but also Artin's conjecture (which can be found in the book by Murty and Murty, or in my recent paper "Theoreme de Chebotarev et densite de Littlewood").
Apr
9
revised Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$
corrected a typo.
Apr
9
awarded  Mortarboard
Apr
9
revised Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$
deleted 323 characters in body
Apr
9
answered Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$
Apr
9
comment Domains with prime ideal theorems
For your function $\pi_D(x)$ to be defined, you need every non-zero prime ideal $P$ to be such that $D/P$ is finite. Since a finite domain is a field, that means that the ting has to be of dimension 1. Therefore your example pretty much cover the whole spectrum of possibility, and I don't such another behavior for $\pi_D(x)$ should be expected. Now, perhaps you would be interested in generalizing your question as follows: take $D$ any domain which is of finite type over $\mathbb Z$, and let $\pi_D(x)$ be the number of maximal ideals $M$ such that $|D/M|<x$ ($D/M$ is finite, Nullstellensatz)
Apr
9
awarded  Enlightened
Apr
9
awarded  Nice Answer
Apr
9
answered Is there a p-adic Sato - Tate conjecture?
Apr
9
answered Why was John Nash's 1950 Game Theory paper such a big deal?
Apr
8
awarded  Necromancer
Apr
7
answered “Understanding” Gal(\bar Q/Q)
Apr
7
comment Why are Goldbach laggards biased towards $2 \mod 6$?
Oh, I didn't notice this whole discussion was old.
Apr
7
comment Is it possible to give a fair assessment of the influence of Bourbaki's “Eléments de mathématique”?
@ToddTrimble Thanks for the reference, a very interesting read.
Apr
6
comment Why are Goldbach laggards biased towards $2 \mod 6$?
@GHfromMO The link you give seems to be broken. I think web.math.princeton.edu/sarnak/MazurLtrMay08.PDF works instead.
Apr
5
comment Is it possible to give a fair assessment of the influence of Bourbaki's “Eléments de mathématique”?
Indeed, it suffices to consider the influence of Bourbaki on his own members (Cartan, Serre, Grothendieck, etc.) with by their own account is fundamental, and the contribution of those members to mathematics.
Apr
5
comment Is it possible to give a fair assessment of the influence of Bourbaki's “Eléments de mathématique”?
@Smaug, I was not for closing. I think I knew about the faire-part de décès, but had completely forgotten. It's fun. But still, the question seems to me a little ill-defined. What is Bourbaki? Is it just the author of the book signed Bourbaki, or is it the sum of its members? In the second case, there is no doubt that mathematical importance of Bourbaki was overwhelming, but I think you meant it more in the first sense. But then the question has a different meaning: how influential Bourbaki was as a teacher, as a text-book author? In this sense as well, the obvious answer is "enormous":
Apr
5
comment Is it possible to give a fair assessment of the influence of Bourbaki's “Eléments de mathématique”?
The problem with the way you formulate the question is that Bourbaki never published a research paper or book. So the question is a little bit like: what the mathematical importance of wikipedia ? If the question is to be understood "how useful are Bourbaki's books for a research mathematician, as compared say, with wikipedia?", then it may make some sense... Also, what happened in 1968 regarding to Bourbaki?
Apr
4
answered Counting solutions modulo primes