13 papers · 1 filter
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…
Sequences of integers generated by two fixed primes
Alessandro Languasco, Florian Luca, Pieter Moree +1
Let and be two distinct fixed prime numbers and the sequence of consecutive integers of the form with . Tijdeman gave a lower bou…
Numerical verification of Littlewood's bounds for
Alessandro Languasco
Let be the Dirichlet -function associated to a non trivial primitive Dirichlet character defined , where is an odd prime. In this paper we introduce a…