کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4665988 | 1633840 | 2013 | 34 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Diophantine approximation of the exponential function and Sondowʼs Conjecture
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We begin by examining a hitherto unexamined partial manuscript by Ramanujan on the diophantine approximation of e2/ae2/a published with his lost notebook. This diophantine approximation is then used to study the problem of how often the partial Taylor series sums of e coincide with the convergents of the (simple) continued fraction of e. We then develop a p-adic analysis of the denominators of the convergents of e and prove a conjecture of J. Sondow that there are only two instances when the convergents of the continued fraction of e coalesce with partial sums of e. We conclude with open questions about the zeros of certain p-adic functions naturally occurring in our proofs.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 248, 25 November 2013, Pages 1298–1331
Journal: Advances in Mathematics - Volume 248, 25 November 2013, Pages 1298–1331
نویسندگان
Bruce C. Berndt, Sun Kim, Alexandru Zaharescu,