期刊
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
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AMER MATHEMATICAL SOC
DOI: 10.1090/tran/8885
关键词
Holomorphic projection; elliptic curves; trace of Frobenius; Hurwitz class numbers
类别
In this paper, we investigate the moments of Hurwitz class numbers in relation to fixed arithmetic progressions of imaginary quadratic orders. Specifically, we examine the ratio of the 2k-th moment to the zeroeth moment for H(4n - t2) as n varies, where t is fixed in an arithmetic progression t = m (mod M). As a consequence, we obtain asymptotic formulas for moments of the trace t = m (mod M) of Frobenius on elliptic curves over finite fields with pr elements when n = pr.
In this paper, we study moments of Hurwitz class numbers associated to imaginary quadratic orders restricted into fixed arithmetic progressions. In particular, we fix t in an arithmetic progression t = m (mod M) and consider the ratio of the 2k-th moment to the zeroeth moment for H(4n - t2) as one varies n. The special case n = pr yields as a consequence asymptotic formulas for moments of the trace t = m (mod M) of Frobenius on elliptic curves over finite fields with pr elements.
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