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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…
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…
Euler constants from primes in arithmetic progression
Alessandro Languasco, Pieter Moree
Many Dirichlet series of number theoretic interest can be written as a product of generating series , with ranging…
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…