The least prime number represented by a binary quadratic form

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Abstract

Let D < 0 be a fundamental discriminant and h(D) be the class number of Q(√D). Let R(X, D) be the number of classes of the binary quadratic forms of discriminant D which represent a prime number in the interval [X, 2X]. Moreover, assume that πD(X) is the number of primes which split in Q(√D) with norm in the interval [X, 2X]. We prove that ( π π(X) D(X) )2 R(X, D) (1 + π(X) h(D) ) , h(D) where π(X) is the number of primes in the interval [X, 2X] and the implicit constant in is independent of D and X.

Original languageEnglish (US)
Pages (from-to)1161-1223
Number of pages63
JournalJournal of the European Mathematical Society
Volume23
Issue number4
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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