12 citations · 20 across the 22 of their papers we have counts for
8 papers · 1 filter
Minimizing GCD sums and applications to non-vanishing of theta functions and to Burgess' inequality
Régis de la Bretèche, Marc Munsch
In recent years the question of maximizing GCD sums regained interest due to its firm link with large values of -functions. In the present paper we initiate the study of minimiz…
Polynomial products modulo primes and applications
Oleksiy Klurman, Marc Munsch
For any polynomial we study arithmetic dynamical systems generated by We apply this to…
Non vanishing of theta functions and sets of small multiplicative energy
Marc Munsch
Let range over the even Dirichlet characters modulo a prime and denote by the associated theta series. The asymptotic behaviour of the second and fourth…
Smooth squarefree and square-full integers in arithmetic progressions
Marc Munsch, Igor E. Shparlinski, Kam Hung Yau
We obtain new lower bounds on the number of smooth squarefree integers up to in residue classes modulo a prime , relatively large compared to , which in some ranges of $p…
The maximum size of short character sums
Marc Munsch
In the present note, we prove new lower bounds on large values of character sums in certain ranges of . Employing an im…
Large values of Dirichlet - functions inside the critical strip
Marc Munsch
In the present paper, we study large values of Dirichlet - functions inside the critical strip. For every , we show that for sufficiently large, there exists a non-…