On p-adic zeros of systems of diagonal forms restricted by a congruence condition
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چکیده
This paper is concerned with non-trivial solvability in p-adic integers of systems of additive forms. Assuming that the congruence equation ax + by + cz ≡ d (mod p) has a solution with xyz 6≡ 0 (mod p) we have proved that any system of R additive forms of degree k with at least 2 · 3R−1 · k + 1 variables, has always non-trivial p-adic solutions, provided p k. The assumption of the solubility of the above congruence equation is guaranteed, for example, if p > k. Hemar Godinho Departamento de Matemática Universidade de Braśılia 70.910-900, Braśılia, DF, Brasil E-mail : [email protected] Paulo H. A. Rodrigues Instituto de Matemática e Estat́ıstica Universidade Federal de Goiás 74.001-970, Goiânia, GO, Brasil E-mail : [email protected] Manuscrit reçu le 21 octobre 2005. The first author was partially supported by a grant of CNPq-Brasil, and the second author was partially supported by a grant of CAPES-PICDT.
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تاریخ انتشار 2007