Averages and moments associated to class numbers of imaginary quadratic fields
For any odd prime 𝓁, let $h𝓁(−d)$ denote the 𝓁-part of the class number of the imaginary quadratic field $Q(√−d)$. Nontrivial pointwise upper bounds are known only for $𝓁 = 3$; nontrivial upper bounds for averagesof $h𝓁(−d)$ have previously been known only for $𝓁 = 3, 5$. In this paper we prove nont...
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| Format: | Journal article |
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London Mathematical Society
2017
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| Summary: | For any odd prime 𝓁, let $h𝓁(−d)$ denote the 𝓁-part of the class number of the imaginary quadratic field $Q(√−d)$. Nontrivial pointwise upper bounds are known only for $𝓁 = 3$; nontrivial upper bounds for averagesof $h𝓁(−d)$ have previously been known only for $𝓁 = 3, 5$. In this paper we prove nontrivial upper bounds for the average of $h𝓁(−d)$ for all primes $𝓁 ≥ 7$, as well as nontrivial upper bounds for certain higher moments for all primes $𝓁 ≥ 3$. |
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