# Joël

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bio website people.brandeis.edu/~jbellaic location Stony Creek, États-Unis age member for 3 years, 7 months seen 27 mins ago profile views 9,799

Professor of Mathematics at Brandeis University

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 Apr9 comment Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$ Je vais le faire. Apr9 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"). Apr9 revised Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$ corrected a typo. Apr9 awarded Mortarboard Apr9 revised Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$ deleted 323 characters in body Apr9 answered Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$ Apr9 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|