Errata to "Average orders of multiplicative arithmetical functions of integer matrices" (Acta Arith. 66 (1994), 45-62)
Errata to: Comparison of regular convolutions.
Errata to “The Dirichlet series of : On an error term associated with its coefficients” (Acta Arith. 75 (1996), 39-69)
Erratum: "On the number of prime divisors of the order of elliptic curves modulo p" (Acta Arith. 117 (2005), 341-352)
Estimates of convolutions of certain number-theoretic error terms.
E-symmetric numbers
A positive integer n is called E-symmetric if there exists a positive integer m such that |m-n| = (ϕ(m),ϕ(n)), and n is called E-asymmetric if it is not E-symmetric. We show that there are infinitely many E-symmetric and E-asymmetric primes.
Etude des nombres 2-hautement composés.
Etude d'un terme d'erreur lié à la fonction totient de Jordan
Étude d'une somme arithmétique multiple liée à la fonction de Möbius
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.
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.