Scholarlink

<p>We generalize the notion of Elkies primes for elliptic curves to the setting of abelian varieties, possibly equipped with real multiplication (RM), and prove the following. Let&#xa0;<i>A</i> be such an abelian variety over a number field whose Galois representation has large image with respect to the chosen RM. Then the distribution of the number of Elkies primes (in a suitable range) for reductions of&#xa0;<i>A</i> modulo primes converges weakly to a Gaussian distribution around its expected value. This refines and generalizes results obtained by Shparlinski and Sutherland in the case of non-CM elliptic curves, and has implications for the complexity of the SEA point counting algorithm for abelian surfaces over finite fields.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The asymptotic distribution of Elkies primes for reductions of abelian varieties is Gaussian

  • 期刊论文

  • 发表日期：

    2025年7月2日

查看全文
  • Alexandre Benoist,
  • Jean Kieffer

摘要

We generalize the notion of Elkies primes for elliptic curves to the setting of abelian varieties, possibly equipped with real multiplication (RM), and prove the following. Let A be such an abelian variety over a number field whose Galois representation has large image with respect to the chosen RM. Then the distribution of the number of Elkies primes (in a suitable range) for reductions of A modulo primes converges weakly to a Gaussian distribution around its expected value. This refines and generalizes results obtained by Shparlinski and Sutherland in the case of non-CM elliptic curves, and has implications for the complexity of the SEA point counting algorithm for abelian surfaces over finite fields.