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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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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
Journal: Journal of Number Theory - Volume 128, Issue 6, June 2008, Pages 1847–1863
نویسندگان
Brittany Brown, Neil J. Calkin, Timothy B. Flowers, Kevin James, Ethan Smith, Amy Stout,