کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4593374 1630650 2016 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Supercongruences and complex multiplication
ترجمه فارسی عنوان
ستاره های بزرگ و ضریب پیچیده
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We study congruences involving truncated hypergeometric series of the formF23(1/2,1/2,1/21,1;λ)(mps−1)/2:=∑k=0(mps−1)/2((1/2)k/k!)3λk where p   is a prime and m,sm,s are positive integers. These truncated hypergeometric series are related to the arithmetic of a family of K3 surfaces. For special values of λ  , with s=1s=1, our congruences are stronger than those predicted by the theory of formal groups, because of the presence of elliptic curves with complex multiplications. They generalize a conjecture made by Stienstra and Beukers for the λ=1λ=1 case and confirm some other supercongruence conjectures at special values of λ.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 164, July 2016, Pages 166–178
نویسندگان
, , , , ,