Average orders of multiplicative arithmetical functions of integer matrices
Average r-rank Artin conjecture
Let Γ ⊂ ℚ * be a finitely generated subgroup and let p be a prime such that the reduction group Γₚ is a well defined subgroup of the multiplicative group ₚ*. We prove an asymptotic formula for the average of the number of primes p ≤ x for which [ₚ*:Γₚ] = m. The average is taken over all finitely generated subgroups , with and , with a range of uniformity for every i = 1,...,r. We also prove an asymptotic formula for the mean square of the error terms in the asymptotic formula with a similar...
Average Value of the Euler Function on Binary Palindromes
We study values of the Euler function φ(n) taken on binary palindromes of even length. In particular, if denotes the set of binary palindromes with precisely 2ℓ binary digits, we derive an asymptotic formula for the average value of the Euler function on .
Averages of Euler products, distribution of singular series and the ubiquity of Poisson distribution
Averages of twisted elliptic L-functions
Banach algebra techniques in the theory of arithmetic functions
For infinite discrete additive semigroups we study normed algebras of arithmetic functions endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for . This involves an extension of Banach algebras of arithmetic functions by introducing weight functions and proving a weighted inversion theorem of Wiener type in the frame of Gelfand’s theory of commutative Banach algebras.
Beatty sequences and multiplicative number theory
Beleuchtung und Beweis eines Satzes aus Legendre's Zahlentheorie [Book]
Bemerkung zu der Arbeit von Herrn H. Bekic.
Bemerkung zu einem Ergebnis von Erdös über befreundete Zahlen.
Bemerkungen über Primzahlen in kurzen Reihen
Bemerkungen zur Arbeit von S. Knapowski und P. Turán.
?ber die Anzahl der Zahlen a2 + b2 in einer arithmetischen Reihe gro?er Differenz.
Beweis des Satzes, dass jede eigentlich primitive quadratische Form unendlich viele Primzahlen darzustellen fähig ist
Biases in the Shanks-Rényi prime number race.
Bilinear form of the remainder term in the Rosser-Iwaniec sieve of dimension ϰ ∈ (1/2,1)
Billiard complexity in the hypercube
We consider the billiard map in the hypercube of . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that is the order of magnitude of the complexity.
Binomial expected values of arithmetical functions.
Bombieri's theorem in short intervals
Bombieri's theorem in short intervals. II.