5 papers
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 Generalized Riemann Hypothesis (GRH) has long defined the expected bounds for the smallest prime in an arithmetic progression and the least quadratic non-residue. However, this…
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…
Relative class numbers and Euler-Kronecker constants of maximal real cyclotomic subfields
Neelam Kandhil, Alessandro Languasco, Pieter Moree +2
The Euler--Kronecker constant of a number field is the ratio of the constant and the residue of the Laurent series of the Dedekind zeta function at . We study the…
The Kummer ratio of the relative class number for prime cyclotomic fields
Neelam Kandhil, Alessandro Languasco, Pieter Moree +2
Kummer's conjecture predicts the asymptotic growth of the relative class number of prime cyclotomic fields. We substantially improve the known bounds of Kummer's ratio under three…
The Brauer-Siegel ratio for prime cyclotomic fields
Neelam Kandhil, Alessandro Languasco, Pieter Moree
The Brauer-Siegel theorem concerns the size of the product of the class number and the regulator of a number field . We derive bounds for this product in case is a prime cyc…