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- W2952802371 abstract "Let $E$ be an elliptic curve defined over ${mathbb Q}$. For a prime $p$ of good reduction for $E$, denote by $e_p$ the exponent of the reduction of $E$ modulo $p$. Under GRH, we prove that there is a constant $C_Ein (0, 1)$ such that $$ frac{1}{pi(x)} sum_{ple x} e_p = 1/2 C_E x + O_Ebig(x^{5/6} (log x)^{4/3}big) $$ for all $xge 2$, where the implied constant depends on $E$ at most. When $E$ has complex multiplication, the same asymptotic formula with a weaker error term $O_E(1/(log x)^{1/14})$ is established unconditionally. These improve some recent results of Freiberg and Kurlberg." @default.
- W2952802371 created "2019-06-27" @default.
- W2952802371 creator A5066542036 @default.
- W2952802371 date "2012-06-26" @default.
- W2952802371 modified "2023-09-27" @default.
- W2952802371 title "The average exponent of elliptic curves modulo $p$" @default.
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- W2952802371 doi "https://doi.org/10.48550/arxiv.1206.5929" @default.
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