Despite its seemingly deterministic nature, the study of whole numbers, especially prime
numbers, has many interactions with probability theory, the theory of random processes and …

We show that for a Steinhaus random multiplicative function f: N→ D and any polynomial P
(x)∈ Z [x] of deg P≥ 2 which is not of the form w (x+ c) d for some w∈ Z, c∈ Q, we have 1 …

We prove that if is a Steinhaus or Rademacher random multiplicative function, there almost
surely exist arbitrarily large values of for which. This is the first such bound that grows faster …

We study the inequities in the distribution of Frobenius elements in Galois extensions of the
rational numbers with Galois groups that are either dihedral D 2 n or (generalized) …

The style of this book is a bit idiosyncratic. The results that interest us belong to number
theory, but the emphasis in the proofs will be on the probabilistic aspects, and on the …

We continue to investigate the race between prime numbers in many residue classes
modulo q, assuming the standard conjectures GRH and LI. We show that provided n/\log q …

Using the same heuristic argument leading to the Lang-Waldschmidt Conjecture in the
theory of linear forms in logarithms, we formulate an effective version of the Linear …

Around eighty years after its birth, the field of probabilistic number theory continues to see
very interesting developments. On the occasion of a thematic program on the subject that …

The thesis mainly focuses on the study of how probabilistic ideas and techniques interact
with arithmetic structures. In analytic number theory, a lot of interesting arithmetic problems …

Let χ be a real and non-principal Dirichlet character, L (s, χ) its Dirichlet L-function and let p
be a generic prime number. We prove the following result: If for some 0≤ σ< 1 the partial …