On the Zeta Function of Forms of Fermat Equations

Details On the Zeta Function of Forms of Fermat Equations On the Zeta Function of Forms of Fermat Equations

2003-01-17

arxiv.org/abs/math/0301186v1

Mathematics

Number Theory

Scientific paper

We study ``forms of the Fermat equation'' over an arbitrary field $k$, i.e. homogenous equations of degree $m$ in $n$ unknowns that can be transformed into the Fermat equation $X_1^m+...+X_n^m$ by a suitable linear change of variables over an algebraic closure of $k$. Using the method of Galois descent, we classify all such forms. In the case that $k$ is a finite field of characteristic greater than $m$ that contains the $m$-th roots of unity, we compute the Galois representation on $l$-adic cohomology (and so in particular the zeta function) of the hypersurface associated to an arbitrary form of the Fermat equation.

Affiliated with

Also associated with

No associations

Rating

On the Zeta Function of Forms of Fermat Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Zeta Function of Forms of Fermat Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Zeta Function of Forms of Fermat Equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585895