Numerical investigations related to the derivatives of the -series of certain elliptic curves.
Odometers and Toeplitz systems revisited in the context of Sarnak's conjecture
Although Sarnak's conjecture holds for compact group rotations (irrational rotations, odometers), it is not even known whether it holds for all Jewett-Krieger models of such rotations. In this paper we show that it does, as long as the model is at the same a topological extension, via the same map that establishes the isomorphism, of an equicontinuous model. In particular, we recover (after [AKL]) that regular Toeplitz systems satisfy Sarnak's conjecture, and, as another consequence, so do...
On integers of the form
On the first sign change in Mertens' theorem
The function is known to change sign infinitely often, but so far all calculated values are positive. In this paper we prove that the first sign change occurs well before exp(495.702833165).
On the order of the Mertens function.
On the Siegel-Tatuzawa-Hoffstein theorem
Polynomials taking prime values. (Polynômes prenant des valeurs premières.)
Random matrix theory and the Fourier coefficients of half-integral weight forms.
Sign changes in
Small limit points of Mahler's measure.
Some interesting series arising from the power series expansion of .
Summatory function of the Möbius function. I: Experimental upper bounds. (Fonction sommatoire de la fonction de Möbius. I: Majorations expérimentales.)
Summatory function of the Möbius function. II: Elementary asymptotic upper bounds. (Fonction sommatoire de la fonction de Möbius. II: Majorations asymptotiques élémentaires.)
The asymptotic distribution of exponential sums. I.
The asymptotic distribution of exponential sums. II.