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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 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…
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…
Euler-Kronecker constants of modular forms: beyond Dirichlet -series
Steven Charlton, Anna Medvedovsky, Pieter Moree
The Euler-Kronecker constants related to congruences of Fourier coefficients of modular forms that have been computed so far, involve logarithmic derivatives of Dirichlet -serie…