2 citations · 6 across the 16 of their papers we have counts for
20 papers · 1 filter
On the friable mean-value of the Erdős-Hooley Delta function
Bruno Martin, Gérald Tenenbaum, Julie Wetzer
For integer and real , define . Then, put We provide uniform uppe…
On simply normal numbers with digit dependencies
Verónica Becher, Agustín Marchionna, Gérald Tenenbaum
Given an integer and a set of prime numbers, the set of Toeplitz numbers comprises all elements of whose digits in the base…
Friable averages of complex arithmetic functions
Régis de la Bretèche, Gérald Tenenbaum
We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some complex power of the Riemann zeta function. We obtain asymptotic expansion…
Note on a conjecture of Hildebrand regarding friable integers
Régis de la Bretèche, Gérald Tenenbaum
Hildebrand proved that the smooth approximation for the number of -friable integers not exceeding holds for under the Riemann hypothesi…
An Erdős-Kac theorem for integers with dense divisors
Gérald Tenenbaum, Andreas Weingartner
We show that for large integers , whose ratios of consecutive divisors are bounded above by an arbitrary constant, the number of prime factors follows an approximate normal dist…
Two upper bounds for the Erdős--Hooley Delta-function
Régis de la Bretèche, Gérald Tenenbaum
For integer and real , let . The Erdős--Hooley Delta-function is then defined by $Δ(n):=\max_{u\in{\…
Friable averages of oscillating multiplicative functions
Régis de la Bretèche, Gérald Tenenbaum
We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some negative power of the Riemann zeta function. We obtain asymptotic expansio…
On the gap distribution of prime factors
Régis de la Bretèche, Gérald Tenenbaum
Let denote the increasing sequence of distinct prime factors of an integer . For , let denote the number of those indexes su…
Remarks on the Selberg--Delange method
Régis de la Bretèche, Gérald Tenenbaum
Let be a complex number and let be a multiplicative arithmetic function whose Dirichlet series takes the form , where is associated to a multip…
Multiplicative functions in large arithmetic progressions and applications
Étienne Fouvry, Gérald Tenenbaum
We establish new Bombieri-Vinogradov type estimates for a wide class of multiplicative arithmetic functions and derive several applications, including: a new proof of a recent esti…
Effective Erd\H os--Wintner theorems
Gérald Tenenbaum, Johann Verwee
The classical theorem of Erd\H os \& Wintner furnishes a criterion for the existence of a limiting distribution for a real, additive arithmetical function. This work is devoted to…
Generalized Mertens sums
Gérald Tenenbaum
Extending a classical estimate of Mertens for the sum of the reciprocals of the first primes, we provide an explicit remainder formula for products of an arbitrary, but fixed, numb…
Some of Erd\H os' unconventional problems in number theory, thirty-four years later
Gérald Tenenbaum
We give an historical account, including recent progress, on some problems of Erd\H os in number theory.
Small Gál sums and applications
Régis de la Bretèche, Marc Munsch, Gérald Tenenbaum
In recent years, maximizing Gál sums regained interest due to a firm link with large values of -functions. In the present paper, we initiate an investigation of small sums of Gá…
A note on the normal largest gap between prime factors
Gérald Tenenbaum
Let denote the increasing sequence of distinct prime factors of an integer . We provide details for the proof of a statement of Erdős implying that, fo…
Power partitions and saddle-point method
Gérald Tenenbaum, Jie Wu, Yali Li
For , denote by the number of partitions of an integer into -th powers. In this note, we apply the saddle-point method to provide a new proof for the…
On local laws for the number of small prime factors
Gérald Tenenbaum
Investigating a question of Alladi, we describe the local distribution of small prime factors of integers, with emphasis on the transition phase occurring for certain values of the…
A remark on Sarnak's conjecture
Régis de la Bretèche, Gérald Tenenbaum
We investigate Sarnak's conjecture on the Möbius function in the special case when the test function is the indicator of the set of integers for which a real additive function assu…
Moyennes effectives de fonctions multiplicatives complexes
Gérald Tenenbaum
We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's clas…
The distribution of integers with at least two divisors in a short interval
Kevin Ford, Gerald Tenenbaum
Let H(x,y,z) be the number of integers with a divisor in (y,z] and let H_1(x,y,z) be the number of integers with exactly one such divisor. When y and z are close, i…