M. G. Mahmoudi: A dichotomy principle for representations of primes by quadratic forms


Submission: 2017, Mar 1

The quadratic value theorem provides a dichotomy principle for the representation of an irreducible polynomial $p$ in the ring $A=F[X_1,\cdots,X_n]$ where $F$ is a field, by an anisotropic quadratic form $q$ defined over $F$: either a scalar multiple of $p$ is multiplicatively generated by the values of $q$ over $A$, or $q$ is anisotropic over the residue field of $A$ at $p$. We examine the validity of this principle in wider contexts.

2010 Mathematics Subject Classification: 11E04, 11E25

Keywords and Phrases: quadratic forms, division algorithm

Full text: dvi.gz 34 k, dvi 80 k, ps.gz 906 k, pdf.gz 174 k, pdf 195 k.

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