کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415592 1630677 2014 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the action of Hecke operators on Drinfeld modular forms
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the action of Hecke operators on Drinfeld modular forms
چکیده انگلیسی

In this paper we determine the explicit structure of the semisimple part of the Hecke algebra that acts on Drinfeld modular forms of full level modulo T. We show that modulo T the Hecke algebra has a non-zero semisimple part. In contrast, a well-known theorem of Serre asserts that for classical modular forms the action of Tℓ for any odd prime ℓ is nilpotent modulo 2. After proving the result for Drinfeld modular forms modulo T, we use computations of the Hecke action modulo T to show that certain powers of the Drinfeld modular form h cannot be eigenforms. Finally, we pose a question a positive answer to which will mean that the Hecke algebra that acts on Drinfeld modular forms of full level is not smooth for large weights, which again contrasts the classical situation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 137, April 2014, Pages 186-200
نویسندگان
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