کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897082 | 1630630 | 2018 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An analytic heuristic for multiplicity computation for Zaremba's Conjecture
ترجمه فارسی عنوان
یک اکتشافی تحلیلی برای محاسبات چندگانه برای گزاره زارمبا
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Zaremba's Conjecture concerns the formation of continued fractions with partial quotients restricted to a given alphabet. In order to answer the numerous questions that arrive from this conjecture, it is best to consider a semi-group, often denoted ÎA, which arises naturally as a subset of SL2(Z) when considering finite continued fractions. To translate back from this semi-group into rational numbers, we select a projection mapping satisfying certain criteria to recover the numerator and denominator of the continued fractions in rational form. The central question of our research is to determine the multiplicity of a given denominator. To this end, we develop a heuristic method similar to the Hardy-Littlewood Circle Method. We compare this theoretical model to the exact data, gleaned by simulation, and demonstrate that our formula appears to be asymptotically valid. We then evaluate different aspects of the accuracy of our formula.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 184, March 2018, Pages 179-191
Journal: Journal of Number Theory - Volume 184, March 2018, Pages 179-191
نویسندگان
Peter Cohen,