Die Primfaktorzerlegung der Werte der Kreisteilungspolynome.
Die Primfaktorzerlegung der Werte der Kreisteilungsprobleme. II.
Die Ramanujan-Entwicklung reellwertiger multiplikativer Funktionen vom Betrage kleiner oder gleich Eins.
Die Reziprozitätsgesetze für Potenzreste mit Primzahlexponenten in algebraischen Zahlkörpern. (Erster Teil)
Die Summe der Reziproken der natürlichen Zahlen ohne Ziffer 9.
Diedergruppe und Reziprozitätsgesetz.
Differences between powers of a primitive root.
Differences of multiple Fibonacci numbers.
Digit sets of integral self-affine tiles with prime determinant
Let M ∈ Mₙ(ℤ) be expanding such that |det(M)| = p is a prime and pℤⁿ ⊈ M²(ℤⁿ). Let D ⊂ ℤⁿ be a finite set with |D| = |det(M)|. Suppose the attractor T(M,D) of the iterated function system has positive Lebesgue measure. We prove that (i) if D ⊈ M(ℤⁿ), then D is a complete set of coset representatives of ℤⁿ/M(ℤⁿ); (ii) if D ⊆ M(ℤⁿ), then there exists a positive integer γ such that , where D₀ is a complete set of coset representatives of ℤⁿ/M(ℤⁿ). This improves the corresponding results of Kenyon,...
Digital expansion of exponential sequences
We consider the -ary digital expansion of the first terms of an exponential sequence . Using a result due to Kiss and Tichy [8], we prove that the average number of occurrences of an arbitrary digital block in the last digits is asymptotically equal to the expected value. Under stronger assumptions we get a similar result for the first digits, where is a positive constant. In both methods, we use estimations of exponential sums and the concept of discrepancy of real sequences modulo ...
Digital expansions in real algebraic quadratic fields.
Digital sum moments and substitutions
Diophantine equation for four prime divisors of
In this paper the special diophantine equation with integer coefficients is discussed and integer solutions are sought. This equation is solved completely just for four prime divisors of .
Diophantine equations and identities.
Diophantine representation of Mersenne and Fermat primes
Diophantine representation of the decimal expansions of and
Discrete planes, -actions, Jacobi-Perron algorithm and substitutions
We introduce two-dimensional substitutions generating two-dimensional sequences related to discrete approximations of irrational planes. These two-dimensional substitutions are produced by the classical Jacobi-Perron continued fraction algorithm, by the way of induction of a -action by rotations on the circle. This gives a new geometric interpretation of the Jacobi-Perron algorithm, as a map operating on the parameter space of -actions by rotations.
Discretization of prime counting functions, convexity and the Riemann hypothesis
We study tails of prime counting functions. Our approach leads to representations with a main term and an error term for the asymptotic size of each tail. It is further shown that the main term is of a specific shape and can be written discretely as a sum involving probabilities of certain events belonging to a perturbed binomial distribution. The limitations of the error term in our representation give us equivalent conditions for various forms of the Riemann hypothesis, for classical type zero-free...
Disjoint covering systems and product-invariant relations
Disjoint covering systems with precisely one multiple modulus