کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4593748 1630669 2014 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On simultaneous diophantine approximations to ζ(2)ζ(2) and ζ(3)ζ(3)
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On simultaneous diophantine approximations to ζ(2)ζ(2) and ζ(3)ζ(3)
چکیده انگلیسی

We present a hypergeometric construction of rational approximations to ζ(2)ζ(2) and ζ(3)ζ(3) which allows one to demonstrate simultaneously the irrationality of each of the zeta values, as well as to estimate from below certain linear forms in 1, ζ(2)ζ(2) and ζ(3)ζ(3) with rational coefficients. We then go further to formalize the arithmetic structure of these specific linear forms by introducing a new notion of (simultaneous) diophantine exponent. Finally, we study the properties of this newer concept and link it to the classical irrationality exponent and its generalizations given recently by S. Fischler.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 145, December 2014, Pages 362–387
نویسندگان
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