Abstract
We compute the density of primes represented by a special quadratic form in a fixed square residue class. Using this result and a new method introduced by Thaine we prove the fact that for a prime p > 3 congruent to 3 modulo 4, the component e (p+1)/2 of the p-Sylow subgroup of the ideal class group of ℚ(ζ p ) is trivial.
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Qin, H., Shen, Q. A density theorem and its application. Sci. China Math. 58, 1621–1626 (2015). https://doi.org/10.1007/s11425-015-4999-z
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DOI: https://doi.org/10.1007/s11425-015-4999-z