On some new congruences for generalized Bernoulli numbers
On some new estimates for h¯(ℚ(ζₚ))
On some non-holonomic sequences.
On some number-theoretic sums introduced by Jacobsthal
On Some Partition Functions Related to Some Mock Theta Functions
We show that some partitions related to two of Ramanujan's mock theta functions are related to indefinite quadratic forms and real quadratic fields. In particular, we examine a third order mock theta function and a fifth order mock theta function.
On some partitions related to .
On some permutation polynomials over finite fields.
On some polynomials allegedly related to the abc conjecture
On some problems in
On some problems involving Hardy’s function
Some problems involving the classical Hardy function , are discussed. In particular we discuss the odd moments of Z(t) and the distribution of its positive and negative values.
On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions ϕ and σ
Let σ(n) denote the sum of positive divisors of the integer n, and let ϕ denote Euler's function, that is, ϕ(n) is the number of integers in the interval [1,n] that are relatively prime to n. It has been conjectured by Mąkowski and Schinzel that σ(ϕ(n))/n ≥ 1/2 for all n. We show that σ(ϕ(n))/n → ∞ on a set of numbers n of asymptotic density 1. In addition, we study the average order of σ(ϕ(n))/n as well as its range. We use similar methods to prove a conjecture of Erdős that ϕ(n-ϕ(n)) < ϕ(n)...
On some problems of W. Sierpiński
On some properties of bivariate Fibonacci and Lucas polynomials.
On some properties of Chebyshev polynomials
Letting (resp. ) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences and for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also and admit remarkableness integer coordinates on each of the two basis.
On some properties of dispersion of block sequences of positive integers
On some properties of the Lüroth-type alternating series representations for real numbers.
On some properties of two simultaneous polygonal sequences.
On Some Relations which are Equivalent to Functional Equations Involving the Riemann Zeta Function.
On some remarkable properties of the two-dimensional Hammersley point set in base 2
We study a special class of -nets in base 2. In particular, we are concerned with the two-dimensional Hammersley net that plays a special role among these since we prove that it is the worst distributed with respect to the star discrepancy. By showing this, we also improve an existing upper bound for the star discrepancy of digital -nets over . Moreover, we show that nets with very low star discrepancy can be obtained by transforming the Hammersley point set in a suitable way.
On Some Results of Atkin and Lehner.