TY - JOUR
T1 - The least prime number represented by a binary quadratic form
AU - Sardari, Naser Talebizadeh
N1 - Publisher Copyright:
© 2021 European Mathematical Society
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85103587547&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85103587547&partnerID=8YFLogxK
U2 - 10.4171/JEMS/1031
DO - 10.4171/JEMS/1031
M3 - Article
AN - SCOPUS:85103587547
SN - 1435-9855
VL - 23
SP - 1161
EP - 1223
JO - Journal of the European Mathematical Society
JF - Journal of the European Mathematical Society
IS - 4
ER -