Papers › Counting Zeros of Dirichlet L-Functions
Counting Zeros of Dirichlet L-Functions
Michael A. Bennett, Greg Martin, Kevin O'Bryant, Andrew Rechnitzer
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We give explicit upper and lower bounds for N(T,χ), the number of zeros of a Dirichlet L-function with character χ and height at most T. Suppose that χ has conductor q>1, and that T≥5/7. If ℓ=log(q(T+2))/2π> 1.567, then | N(T,χ) - ( T/π logqT/2πe -(χ(-1))/4) | ≤0.22737 ℓ+ 2 log(1+ℓ) - 0.5. We give slightly stronger results for small q and T. Along the way, we prove a new bound on |L(s,χ)| for σ<-1/2.
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