Posted in
Speaker:
Naser Talebizadeh Sardari
Affiliation:
MPIM
Date:
Wed, 27/11/2019 - 14:30 - 15:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar 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 π_D(X) is the number of primes, which split in ℚ(√D) with norm in the interval [X,2X]. We prove that (π_D(X)/π(X))
2 ≪ R(X,D)/h(D) (1+h(D)/π(X)), where π(X) is the number of primes in the interval [X,2X] and the implicit constant in ≪ is independent of D and X.
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