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Beyond the Riemann Hypothesis bounds: A pair-correlation approach to the least prime in arithmetic progression and the smallest quadratic non-residue
Neelam Kandhil, Alessandro Languasco, Pieter Moree
The paper shows that using the pair‑correlation (vertical spacing) of zeros of Dirichlet L‑functions together with the Generalized Riemann Hypothesis yields improved bounds for the…
Pair Correlation of zeros of Dirichlet -Functions: A possible path towards the conjectures of Chowla, Elliott-Halberstam and Montgomery
Neelam Kandhil, Alessandro Languasco, Pieter Moree
Assuming the Generalized Riemann Hypothesis and a pair correlation conjecture for the zeros of Dirichlet -functions, we establish the truth of a conjecture of Montgomery (in its…
Counting ideals in abelian number fields
Alessandro Languasco, Rashi Lunia, Pieter Moree
Already Dedekind and Weber considered the problem of counting integral ideals of norm at most in a given number field . Here we improve on the existing results in case $K/\m…