Errata to the paper: ``Remarks on maximum and minimum exponents in factoring'
Erweiterung eines Satzes von Schinzel über Potenzreste
Essentially different factorizations of a natural number
Estimates for the sequence of primes.
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.
Étude bibliographique. Sur la théorie des nombres
Etude d'un terme d'erreur lié à la fonction totient de Jordan
Étude sur la théorie des résidus cubiques.
Euler indicators of binary recurrence sequences.
Euler's function and the sum of divisors.
Evaluation effective du nombre d'entiers n tels que φ(n) ≤ x
Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
The convolution sum, [...] ∑(l,m)∈N02αl+βm=nσ(l)σ(m), where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms are used to achieve these evaluations. Since the modular space of level 22 is contained in that of level 44, we almost completely use the basis elements of the modular space of level 44 to carry out the evaluation of the convolution sums for αβ = 22. We then use these convolution sums to determine formulae for the number of representations of a positive integer by...
Evaluation of the sums
The convolution sum is evaluated for and all . This completes the partial evaluation given in the paper of J. G. Huard, Z. M. Ou, B. K. Spearman, K. S. Williams.
Evaluations of the Rogers-Ramanujan continued fraction R(q) by modular equations
Even perfect numbers and their Euler's function.
Exact exponent in the remainder term of Gelfond's digit theorem in the binary case
Exact m-covers and the linear form
Exact Solution of Linear Equations Using P-Adic Expansions
Experimental results on probable primality.
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.,