Diphantine Approximation with Square-free Numbers.
Écarts entre nombres premiers successifs
Le théorème des nombres premiers dit que la distance entre deux nombres premiers consécutifs est, en moyenne, de l’ordre de . Récemment, D. Goldston, J. Pintz et C. Yıldırım sont parvenus à démontrer que la distance normalisée pouvait devenir arbitrairement petite, améliorant spectaculairement les résultats connus auparavant. Sous des hypothèses considérées comme raisonnables, ils parviennent à montrer que infiniment souvent. Leur méthode est une très jolie application d’idées inspirée par...
Eigenvalues in the large sieve inequality, II
We explore numerically the eigenvalues of the hermitian formwhen . We improve on the existing upper bound, and produce a (conjectural) plot of the asymptotic distribution of its eigenvalues by exploiting fairly extensive computations. The main outcome is that this asymptotic density most probably exists but is not continuous with respect to the Lebesgue measure.
Eine Anwendung der Selbergschen Siebmethode in algebraischen Zahlkörpern
Eine Bemerkung zum Sieb des Eratosthenes.
Factor tables 1657–1817, with notes on the birth of number theory
The history of the construction, organisation and publication of factor tables from 1657 to 1817, in itself a fascinating story, also touches upon many topics of general interest for the history of mathematics. The considerable labour involved in constructing and correcting these tables has pushed mathematicians and calculators to organise themselves in networks. Around 1660 J. Pell was the first to motivate others to calculate a large factor table, for which he saw many applications, from Diophantine...
Factoring integers with large-prime variations of the quadratic sieve.
Farey fractions with prime denominator and the large sieve
Fast-Primzahlen in kurzen Intervallen.
Gaps between primes in Beatty sequences
We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).
Halving an estimate obtained from Selberg's upper bound method
Hilbert's inequality and the large sieve
Improving on the Brun-Titchmarsh theorem
Incomplete sums of non-negative multiplicative functions
Iwaniec's bilinear form of the error term in the Selberg sieve
Kloosterman Sums and Fourier Coefficients of Cusp Forms.
La «nouvelle technique» de Hooley
Large sieve inequality with characters to square moduli
Le crible à vecteurs
Lower bounds for expressions of large sieve type
We show that the large sieve is optimal for almost all exponential sums.