# Sanchez

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I really appreciate it when you take time to answer my questions. Thanks!

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 Feb7 accepted Irreducible homogeneous polynomial over $\mathbb{Z}$ staying irreducible modulo large primes Feb7 answered Proving the Jacobi sum $J(\chi,\rho)=\sum_{t\in F_p}\chi(1-t^2)$ when $\rho$ has order $2$? Feb6 comment How many primes can lie over a prime? Yes, actually it's right. Not sure why this happens again, haha. Feb6 comment How many primes can lie over a prime? @MartinBrandenburg, actually that was a clearly wrong remark, not sure what I was thinking. Feb6 revised How many primes can lie over a prime? deleted 165 characters in body Feb6 comment How many primes can lie over a prime? @MartinBrandenburg, $S$ is a noetherian $R$-module. Feb6 revised How many primes can lie over a prime? added 497 characters in body Feb6 comment How many primes can lie over a prime? @JacobSchlather Oh, sorry for mixing up the yes's and no's. I will add some details about cyclotomic extensions part. Feb6 answered How many primes can lie over a prime? Feb6 comment Irreducible homogeneous polynomial over $\mathbb{Z}$ staying irreducible modulo large primes Thanks! I will read your answer in detail later, but there's one thing I want to clarify. In the book I am reading (Browning's book on qualitative arithmetic of varieties), Lang-Weil estimate is only stated for irreducible affine varieties. I have two questions: 1. Does the estimate hold for any variety? In particular, do I need anything like quasi-compactness? 2. Is the bound uniform in some variables, if I consider only the geometrically irreducible varieties? Feb6 awarded Fanatic Feb5 revised Irreducible homogeneous polynomial over $\mathbb{Z}$ staying irreducible modulo large primes added 69 characters in body Feb5 asked Irreducible homogeneous polynomial over $\mathbb{Z}$ staying irreducible modulo large primes Feb4 awarded Nice Answer Feb1 comment The zeta-function of Fibonacci sequence? There is a reason to consider zeta function for the sequence "number of points of a variety mod p^n". I'm not sure if the zeta function for a general sequence is of interest. Feb1 comment The zeta-function of Fibonacci sequence? It looks right. Can you give a reference on zeta function on a sequence in general? Jan31 comment Why should the tangent bundle of the boundary of a conctractible manifold be stably trivial? and the normal bundle is trivial, no?(Fix a metric, and take the unit outward vector field) Jan31 comment for any $a$ belongs to $\mathbb{C}$ $f(z_i)=a$ holds for $z_1,z_2,..;z_n$ Show that $\infty$ is not an essential singularity for $f$ using Picard. This will force $f$ to be a polynomial. Degree $n$ comes from your condition. Jan31 comment Open Subgroups of Affine algebraic groups You say it's connected - then $H$ should be the same as $G$, since the union of all other cosets of $H$ form an open set disjoint from $H$. Jan31 answered Inequality. $\frac{x^3}{y^2+z^2}+\frac{y^3}{z^2+x^2}+\frac{z^3}{x^2+y^2} \geq \dfrac{3}{2}.$