کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4595126 1335799 2008 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
K. Saito's Conjecture for nonnegative eta products and analogous results for other infinite products
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
K. Saito's Conjecture for nonnegative eta products and analogous results for other infinite products
چکیده انگلیسی

We prove that the Fourier coefficients of a certain general eta product considered by K. Saito are nonnegative. The proof is elementary and depends on a multidimensional theta function identity. The z=1 case is an identity for the generating function for p-cores due to Klyachko [A.A. Klyachko, Modular forms and representations of symmetric groups, J. Soviet Math. 26 (1984) 1879–1887] and Garvan, Kim and Stanton [F. Garvan, D. Kim, D. Stanton, Cranks and t-cores, Invent. Math. 101 (1990) 1–17]. A number of other infinite products are shown to have nonnegative coefficients. In the process a new generalization of the quintuple product identity is derived.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 128, Issue 6, June 2008, Pages 1731-1748