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.

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