Remarks on Invariant Measures for Number Theoretic Transformations.
Remarks on maximum and minimum exponents in factoring
Remarks on normal bases
We prove that any Galois extension of a commutative ring with a normal basis and abelian Galois group of odd order has a self-dual normal basis. We apply this result to get a very simple proof of nonexistence of normal bases for certain extensions which are of interest in number theory.
Remarks on number theory I. On primitive α-abundant numbers
Remarks on number theory II. Some problems on the σ function
Remarks on number theory III. On addition chains
Remarks on Ramanujan's inequality concerning the prime counting function
In this paper we investigate Ramanujan’s inequality concerning the prime counting function, asserting that for sufficiently large. First, we study its sharpness by giving full asymptotic expansions of its left and right hand sides expressions. Then, we discuss the structure of Ramanujan’s inequality, by replacing the factor on its right hand side by the factor for a given , and by replacing the numerical factor by a given positive . Finally, we introduce and study inequalities analogous...
Remarks on self-affine tilings.
Remarks on several types of convergence of bounded sequences
In this paper we analyze relations among several types of convergences of bounded sequences, in particulars among statistical convergence, -convergence, -convergence, almost convergence, strong -Cesàro convergence and uniformly strong -Cesàro convergence.
Remarks on some new applications of the dispersion method
Remarks on some number-theoretical functional equations.
Remarks on statistical independence of sequences
Remarks on Steinhaus’ property and ratio sets of sets of positive integers
This paper is closely related to an earlier paper of the author and W. Narkiewicz (cf. [7]) and to some papers concerning ratio sets of positive integers (cf. [4], [5], [12], [13], [14]). The paper contains some new results completing results of the mentioned papers. Among other things a characterization of the Steinhaus property of sets of positive integers is given here by using the concept of ratio sets of positive integers.
Remarks on strongly modular Jacobian surfaces
In [3] we introduced the concept of strongly modular abelian variety. This note contains some remarks and examples of this kind of varieties, especially for the case of Jacobian surfaces, that complement the results of [3].
Remarks on sum of products of -twisted Euler polynomials and numbers.
Remarks on systems of congruence classes
Remarks on the arithmetic properties of the values of hypergeometric functions
Remarks on the differences between consecutive primes.
Remarks on the Ergodic Theory of the Continued Fractions
Remarks on the Irrationality and Transcendence of Certain Series.