Zeros of p-adic forms
نویسنده
چکیده
A variant of Brauer’s induction method is developed. It is shown that quartic p-adic forms with at least 9127 variables have non-trivial zeros, for every p. For odd p considerably fewer variables are needed. There are also subsidiary new results concerning quintic forms, and systems of forms.
منابع مشابه
Behavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups
We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups. We prove Arthur's conjecture, the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group, for quasi-split special unitary groups and their inner forms. Furthermore, we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms. This w...
متن کامل2-Adic zeros of diagonal forms and distance pebbling of graphs
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...
متن کاملA Hasse Principle for Quadratic Forms over Function Fields
We describe the classical Hasse principle for the existence of nontrivial zeros for quadratic forms over number fields, namely, local zeros over all completions at places of the number field imply nontrivial zeros over the number field itself. We then go on to explain more general questions related to the Hasse principle for nontrivial zeros of quadratic forms over function fields, with referen...
متن کاملThe Expected Number of Zeros of a Ran- Dom System of P -adic Polynomials
We study the simultaneous zeros of a random family of d polynomials in d variables over the p-adic numbers. For a family of natural models, we obtain an explicit constant for the expected number of zeros that lie in the d-fold Cartesian product of the p-adic integers. Considering models in which the maximum degree that each variable appears is N , this expected value is pdblogp Nc ( 1 + p−1 + p...
متن کاملCOMPUTATION OF THE ZEROS OF p-ADIC ¿FUNCTIONS. II
The authors have carried out a computational study of the zeros of Kubota-Leopoldt p-adic L-functions. Results of this study have appeared recently in a previous article. The present paper is a sequel to that article, dealing with the computation of the zeros under certain conditions that complicate the original situation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010