On the singular Drinfeld modules of rank 2.
On the singular set, the resolvent and Fermi's Golden Rule for finite volume hyperbolic surfaces.
On the singularities of multiple L-functions
We investigate the singularities of a class of multiple L-functions considered by Akiyama and Ishikawa [2].
On the size of dissociated bases.
On the size of integer solutions of elliptic equations, II
On the size of L(1,χ) and S. Chowla's hypothesis implying that L(1,χ) > 0 for s > 0 and for real characters χ
We give explicit constants κ such that if χ is a real non-principal Dirichlet character for which L(1,χ) ≤ κ, then Chowla's hypothesis is not satisfied and we cannot use Chowla's method for proving that L(s,χ) > 0 for s > 0. These constants are larger than the previous ones κ = 1- log 2 = 0.306... and κ = 0.367... we obtained elsewhere.
On the size of prime factors of integers
On the size of the first factor of the class number of a cyclotomic field.
On the size of zeros of quadratic forms over rational function fields.
On the slopes of the operator acting on overconvergent modular forms
We show that the slopes of the operator acting on 5-adic overconvergent modular forms of weight with primitive Dirichlet character of conductor 25 are given by eitherdepending on and .We also prove that the space of classical cusp forms of weight and character has a basis of eigenforms for the Hecke operators and which is defined over .
On the smallest pseudopower
On the smallest solution to the general binary quadratic diophantine equation
On the solutions of certain diagonal quadratic equations and Lang's conjecture
On the solutions of diophantine equations in units
On the solutions of .
On the Solvability of a Certain Class of Non-Pellian Equations.
On the spaces of Eisenstein series of Hilbert modular groups.
On the spacing between terms of generalized Fibonacci sequences
For k ≥ 2, the k-generalized Fibonacci sequence is defined to have the initial k terms 0,0,...,0,1 and be such that each term afterwards is the sum of the k preceding terms. We will prove that the number of solutions of the Diophantine equation (under some weak assumptions) is bounded by an effectively computable constant depending only on c.
On the special solutions of an equation in a finite field.
On the spectrum of the Thue-Morse quasicrystal and the rarefaction phenomenon
The spectrum of a weighted Dirac comb on the Thue-Morse quasicrystal is investigated by means of the Bombieri-Taylor conjecture, for Bragg peaks, and of a new conjecture that we call Aubry-Godrèche-Luck conjecture, for the singular continuous component. The decomposition of the Fourier transform of the weighted Dirac comb is obtained in terms of tempered distributions. We show that the asymptotic arithmetics of the -rarefied sums of the Thue-Morse sequence (Dumont; Goldstein, Kelly and Speer; Grabner;...