We obtain an asymptotic formula for all moments of Dirichlet $ L $-functions $ L (1,\chi) $
modulo $ p $ when averaged over a subgroup of characters $\chi $ of size $(p-1)/d $ with …

We investigate the distribution of values of cubic Dirichlet LL‐functions at s= 1 s=1.
Following ideas of Granville and Soundararajan for quadratic LL‐functions, we model the …

In a family of Sd+ 1-fields (d= 2, 3, 4), we obtain the conjectured upper and lower bounds of
the residues of Dedekind zeta functions except for a density zero set. For S5-fields, we need …

For a primitive Dirichlet character $\chi $ modulo $ q $, we define $ M (\chi)=\max _ {t}|\sum _
{n\leq t}\chi (n)| $. In this paper, we study this quantity for characters of a fixed odd order …

We investigate the reduction of factoring of squarefree positive integers coprime to 6 to
computing exponents of points on an elliptic curve $ E (\mathbb Z _n) $ over the ring …

We prove two bounds for discrete moments of Weyl sums. The first one can be obtained
using a standard approach. The second one involves an observation how this method can …

For a primitive Dirichlet character $\chi $ modulo $ q $, we define $ M (\chi)=\max_ {t}|\sum_
{n\leq t}\chi (n)| $. In this paper, we study this quantity for characters of a fixed odd order …

A heuristic in analytic number theory stipulates that sets of positive integers cannot
simultaneously be additively and multiplicatively structured. The practical verification of this …

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Stonehouse, Gloucestershire, is in the Stroudwater cloth industry district, and any population
sample taken in the early-modern period might be expected to show numerical and social …