58,366 research outputs found
-adic Zeros of Quintic Forms
It is shown that a quintic form over a p-adic field with at least 26
variables has a non-trivial zero, providing that the cardinality of the residue
class field exceeds 9.Comment: Minor correction
Quartic Forms in Many Variables
We show that a quartic -adic form with at least variables possesses
a non-trivial zero. We also prove new results on systems of cubic, quadratic
and linear forms. As an example, we show that for a system comprising two cubic
forms variables are sufficient.Comment: 8 page
Two applications of the curve lemma for orthogonal groups
We show (under some hypothesis in small dimensions) that the analytic degree
of the divisor of a modular form on the orthogonal group O(2,p) is determined
by its weight. Moreover, we prove that certain integrals, occurring in Arakelov
intersection theory, associated with modular forms on O(2,p) converge.Comment: 16 page
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