کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9515582 | 1343464 | 2005 | 30 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Cranks and dissections in Ramanujan's lost notebook
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
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چکیده انگلیسی
In his lost notebook, Ramanujan offers several results related to the crank, the existence of which was first conjectured by F. J. Dyson and later established by G.E. Andrews and F.G. Garvan. Using an obscure identity found on p. 59 of the lost notebook, we provide uniform proofs of several congruences in the ring of formal power series for the generating function F(q) of cranks. All are found, sometimes in abbreviated form, in the lost notebook, and imply dissections of F(q). Consequences of our work are interesting new q-series identities and congruences in the spirit of Atkin and Swinnerton-Dyer.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 109, Issue 1, January 2005, Pages 91-120
Journal: Journal of Combinatorial Theory, Series A - Volume 109, Issue 1, January 2005, Pages 91-120
نویسندگان
Bruce C. Berndt, Heng Huat Chan, Song Heng Chan, Wen-Chin Liaw,