کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4594118 1630676 2014 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Modules with many non-associates and norm form equations with many families of solutions
ترجمه فارسی عنوان
ماژول ها با بسیاری از غیرمجازات و معادلات معمولی، با معادلات بسیاری از خانواده های راه حل ها شکل می گیرند
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

For every number field KK, with [K:Q]⩾3[K:Q]⩾3, we show that the number of non-associates of the same norm in a full module in KK does not depend only on KK, but can also depend on the module itself. As a corollary, the same can be true for the number of families of solutions of degenerate norm form equations. So the uniform bound obtained by Schmidt for the number of solutions in the non-degenerate case does not hold always here. For three-variable norm forms not arising from full modules, we do obtain a Schmidt-type bound for the number of families of solutions that, together with the above result, completes this aspect of the study of three-variable norm forms.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 138, May 2014, Pages 20–36
نویسندگان
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