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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{\…
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…
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.