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

mmahmoudi@sharif.ir

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

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