On {p}-adic zeros of systems of diagonal forms restricted by a congruence condition
نویسندگان
چکیده
منابع مشابه
On p-adic zeros of systems of diagonal forms restricted by a congruence condition
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...
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The purpose of this article is threefold. Our first two goals are to prove two theorems, one in the field of 2-adic solubility of forms and another in the field of graph pebbling. Our third purpose is to show that while these two theorems may be in different areas, their proofs are essentially the same. Thus we will show that there is an interesting connection between some number theoretical st...
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In this paper we consider systems of diagonal forms with integer coefficients in which each form has a different degree. Every such system has a nontrivial zero in every p-adic field Qp provided that the number of variables is sufficiently large in terms of the degrees. While the number of variables required grows at least exponentially as the degrees and number of forms increase, it is known t...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2007
ISSN: 1246-7405
DOI: 10.5802/jtnb.582