کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4593120 1630644 2017 43 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Sums of divisors functions and Bessel function series
ترجمه فارسی عنوان
مقادیر توابع مقسوم علیه و سری تابع Bessel
کلمات کلیدی
توابع Bessel ؛ مسئله CIRCLE؛ مسئله مقسوم علیه؛ مقادیر Riesz ؛ مقدار تابع مقسوم علیه
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

On page 335 in his lost notebook, Ramanujan recorded without proofs two identities involving finite trigonometric sums and doubly infinite series of Bessel functions. These two identities are intimately connected with the classical circle and divisor problems  , respectively. There are three possible interpretations for the double series of these identities. The first identity has been proved under all three interpretations, and the second under two of them. Furthermore, several analogues of them were established, and they were extended to Riesz sum identities as well. In this paper, we provide analogous Riesz sum identities for the weighted sums of divisors functions, and in particular two of them yield a generalization of the Riesz sum identity for r6(n)r6(n), where r6(n)r6(n) denotes the number of representations of n as a sum of six squares.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 170, January 2017, Pages 142–184
نویسندگان
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