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Extreme values of argL(1,χ)

100%

Lamzouri Y.

Acta Arithmetica

2011

tom 146

nr 4

335-354

On the distribution of the partial sum of Euler's totient function in residue classes

51%

Lamzouri Y., Phaovibul M., Zaharescu A.

Colloquium Mathematicum

2011

tom 123

nr 1

115-127

We investigate the distribution of $Φ(n) = 1+ ∑_{i=1}ⁿ φ(i)$ (which counts the number of Farey fractions of order n) in residue classes. While numerical computations suggest that Φ(n) is equidistributed modulo q if q is odd, and is equidistributed modulo the odd residue classes modulo q when q is even, we prove that the set of integers n such that Φ(n) lies in these residue classes has a positive lower density when q = 3,4. We also provide a simple proof, based on the Selberg-Delange method, of a result of T. Dence and C. Pomerance on the distribution of φ(n) modulo 3.

Ograniczanie wyników

1 Acta Arithmetica

1 Colloquium Mathematicum

2 Lamzouri Y.

1 Phaovibul M.

1 Zaharescu A.

2 2011

Wyniki wyszukiwania

Extreme values of argL(1,χ)

On the distribution of the partial sum of Euler's totient function in residue classes