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The least prime number represented by a binary quadratic form

Posted in
Speaker: 
Naser Talebizadeh Sardari
Affiliation: 
MPIM
Date: 
Wed, 2019-11-27 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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