Journal of Number Theory

This is a reprozip archive containing steps to generate a cyclic modular polynomial for Q(\sqrt{5}). This allows to check the full polynomials that were computed from this step using rational function interpolation.

This code provides algorithms related to computations of total obstruction to the Hasse norm principle.

We compute the values of Mertens' product over prime in an arithmetic progression a mod q, q < = 100, (a,q)=1, with an accuracy of 100 decimal digits. [08 May 2024: Adapted to work with the most recent version of pari/gp (2.16.2)]

We compute the values of Mertens' product over prime in an arithmetic progression a mod q, q < = 100, (a,q)=1, with an accuracy of 100 decimal digits

We compute the values of Mertens' product over prime in an arithmetic progression a mod q, q < = 100, (a,q)=1, with an accuracy of 100 decimal digits

The programs here presented compute max | L(1,chi) | and min |L(1,chi)| over the non-principal primitive Dirichlet characters chi mod q, q prime. These values are then compared with Littlewood's classical estimates and recent ones by Lamzouri-Li-Soundararajan. In the paper the whole range 3<=q<=10^7 is studied; in this capsule are used just few primes (listed in the attached primes.txt file) to contain the running time in few seconds. Required packages are: pari/gp, gp2c, FFTW and a C compiler. More details here: https://doi.org/10.1016/j.jnt.2020.12.017; https://www.math.unipd.it/~languasc/Lcomp/How_it_works.txt ; https://www.math.unipd.it/~languasc/Littlewood_ineq.html