Multiplicative functions satisfying the equation $f(m^2+n^2)=f(m^2)+f(n^2)$

In this paper we establish the distribution of prime numbers in a given arithmetic progression $p \equiv l (m o d k)$ for which $a p + b$ is squarefree.

Multiplicative functions and $k$ -automatic sequences

Soroosh Yazdani (2001)

Journal de théorie des nombres de Bordeaux

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A sequence is called $k$ -automatic if the $n$ ’th term in the sequence can be generated by a finite state machine, reading $n$ in base $k$ as input. We show that for many multiplicative functions, the sequence ${(f (n) mod v)}_{n \geq 1}$ is not $k$ -automatic. Among these multiplicative functions are $γ_{m} (n), σ_{m} (n), μ (n)$ et $φ (n)$ .

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Multiplicative functions and k -automatic sequences

Displaying similar documents to “Multiplicative functions satisfying the equation $f (m^{2} + n^{2}) = f (m^{2}) + f (n^{2})$ ”

Multiplicative functions and $k$ -automatic sequences