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.
Exotic approximate identities and Maass forms
We obtain some approximate identities whose accuracy depends on the bottom of the discrete spectrum of the Laplace-Beltrami operator in the automorphic setting and on the symmetries of the corresponding Maass wave forms. From the geometric point of view, the underlying Riemann surfaces are classical modular curves and Shimura curves.
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.
Extension aux nombres premiers complexes des théorèmes de M. Tchebicheff
Extension of Estermann’s theorem to Euler products associated to a multivariate polynomial
Given a multivariate polynomial with integral coefficients verifying an hypothesis of analytic regularity (and satisfying ), we determine the maximal domain of meromorphy of the Euler product and the natural boundary is precisely described when it exists. In this way we extend a well known result for one variable polynomials due to Estermann from 1928. As an application, we calculate the natural boundary of the multivariate Euler products associated to a family of toric varieties.
Extensions of asymptotic expansions from Chapter 15 of Ramanujan's second notebook.
Extensions of some formulae of A. Selberg.
Extremal orders of compositions of certain arithmetical functions.
Extreme values of symmetric power L-functions at 1
Facteurs premiers d'entiers en progression arithmétique
Facteurs premiers d'entiers en progression arithmétique