Etude d'un terme d'erreur lié à la fonction totient de Jordan
Eulerprodukte und diskrete Mittelwerte.
Euler's function and the sum of divisors.
Évaluation asymptotique de l'ordre maximum d'un élément du groupe symétrique
Evaluation effective du nombre d'entiers n tels que φ(n) ≤ x
Évaluations asymptotiques concernant des fonctions multiplicatives définies sur certains semi-groupes
Exceptional sets in Waring's problem: two squares and s biquadrates
Let denote the number of representations of the positive number n as the sum of two squares and s biquadrates. When or 4, it is established that the anticipated asymptotic formula for holds for all with at most exceptions.
Expansions of binary recurrences in the additive base formed by the number of divisors of the factorial
We note that every positive integer N has a representation as a sum of distinct members of the sequence , where d(m) is the number of divisors of m. When N is a member of a binary recurrence satisfying some mild technical conditions, we show that the number of such summands tends to infinity with n at a rate of at least c₁logn/loglogn for some positive constant c₁. We also compute all the Fibonacci numbers of the form d(m!) and d(m₁!) + d(m₂)! for some positive integers m,m₁,m₂.
Explicit estimates for the summatory function of Λ(n)/n from the one of Λ(n)
We prove that the error term differs from (ψ(x)-x)/x by a well controlled function. We deduce very precise numerical results from the formula obtained.
Explicit estimates on the summatory functions of the Möbius function with coprimality restrictions
We prove that for every x > q ≥ 1, and similar estimates for the Liouville function. We also give better constants when x/q is large.,
Explicit upper bounds for the average order of and application to class number.
Exponential sums involving the largest prime factor function
Exponential sums with multiplicative coefficients.
Exponential Sums with Multiplicative Coefficients.
Extensions of asymptotic expansions from Chapter 15 of Ramanujan's second notebook.