The least prime number represented by a binary quadratic form
Naser Talebizadeh Sardari
Max-Planck-Institut für Mathematik, Bonn, Germany
![The least prime number represented by a binary quadratic form cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-23-issue-4.png&w=3840&q=90)
Abstract
Let be a fundamental discriminant and be the class number of the imaginary quadratic field . Let be the number of the classes of the binary quadratic forms of discriminant which represent a prime number in the interval []. Moreover, assume that is the number of primes which split in with norm in the interval []. We prove that
where is the number of the primes is the number of primes in the interval [] and the implicit constant in is independent of and .
Cite this article
Naser Talebizadeh Sardari, The least prime number represented by a binary quadratic form. J. Eur. Math. Soc. 23 (2021), no. 4, pp. 1161–1223
DOI 10.4171/JEMS/1031