کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4595133 1335799 2008 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Elliptic curves, modular forms, and sums of Hurwitz class numbers
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Elliptic curves, modular forms, and sums of Hurwitz class numbers
چکیده انگلیسی

Let H(N)H(N) denote the Hurwitz class number. It is known that if p is a prime, then∑|r|<2pH(4p−r2)=2p. In this paper, we investigate the behavior of this sum with the additional condition r≡c(modm). Three different methods will be explored for determining the values of such sums. First, we will count isomorphism classes of elliptic curves over finite fields. Second, we will express the sums as coefficients of modular forms. Third, we will manipulate the Eichler–Selberg trace formula for Hecke operators to obtain Hurwitz class number relations. The cases m=2,3m=2,3 and 4 are treated in full. Partial results, as well as several conjectures, are given for m=5m=5 and 7.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 128, Issue 6, June 2008, Pages 1847–1863
نویسندگان
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