On a paper by Nikolaev

The Ramanujan Journal - The purpose of this note is to point out that the paper On algebraic values of function $$ exp (2pi i x + log log y)$$ by Igor Nikolaev published in the Ramanujan...     

On a paper by Khan and Majumdar

In this paper we generalize two results of Khan and Majumdar on the weak sequential convergence of functions in the Lebesgue-Bochner space L_X¹(Ω) and on a Fatou-like convergence theorem.     

On the conjectures of Mordell and Lang in positive characteristics

Oblatum 15-VI-1990 &; 29-XI-1990     

On a paper of S S Pillai

In 1935, Erdös proved that all natural numbers can be written as a sum of a square of a prime and a square-free number. In 1939, Pillai derived an asymptotic formula for the number of such representations. The mathematical review of Pillai’s paper stated that the proof of the above result contained inaccuracies, thus casting a doubt on the correctness of the paper. In this paper, we re-examine Pillai’s paper and show that his argument was essentially correct. Afterwards, we improve the error term in Pillai’s theorem using the Bombieri–Vinogradov theorem.     

On a paper of A. Feldzamen

Results of A. Feldzamen on semi-similarity of operators are proved here using matrix methods. The use of these methods yields simpler proofs, the formulations of the theorems assume a more transparent form. The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research of the Air Research and Development Command United States Air Force through its European Office.     

On a paper of lake about infinite graphs

Lake has constructed graphs G and H such that H contains n disjoint subgraphs isomorphic to G for each positive integer n but H does not contain infinitely many disjoint subgraphs isomorphic to G. Here a concrete example of such graphs with H the lattice points of the plane is given.     

On a paper of Krupchyk, Tarkhanov, and Tuomela

We compare the above-mentioned article with the content of a previous publication.     

On a paper by A. G. Ramm

Si migliorano i risultati di [7].     

On a paper of Hasse concerning the Eisenstein reciprocity law

In the present paper, necessary and sufficient conditions are given for the equality of the power rezidue symbols ( \fracaa )_n {\left( {\frac{\alpha }{a}} \right)_n} and ( \fracaa )_n {\left( {\frac{\alpha }{a}} \right)_n} in the cyclotomic field ℚ(ζ _n ), 2 ∤ n, for a ∈ ℤ, (a, n) = 1. This result is a generalization of the classical Eisenstein reciprocity law and its continuation in a Hasse’s paper. Bibliography: 3 titles.     

Subspace Lang conjecture and some remarks on a transcendental criterion

Let \(b\ge 2\) be an integer and \(\alpha \) is a non-zero real number written in b-ary expansion. Adamczewski et al. (C. R. Acad. Sci. Paris 339 (2004) 11–14) provided a criterion for an irrational number to be a transcendental number using b-ary expansion. In this paper, we make some remarks on this criterion and, under the assumption of Subspace Lang Conjecture, we extend this criterion for a much wider class of irrational numbers.     

Intersections of polynomial orbits, and a dynamical Mordell–Lang conjecture

We prove that if nonlinear complex polynomials of the same degree have orbits with infinite intersection, then the polynomials have a common iterate. We also prove a special case of a conjectured dynamical analogue of the Mordell–Lang conjecture. Mathematics Subject Classification (1991) Primary 14G25; Secondary 37F10, 11C08     

Lang maps and Harris’s conjecture

We show that any variety in characteristic 0 possesses a universal dominant rational map, which we callthe Lang map, to a variety of general type. We discuss a conjecture of J. Harris regarding the relation between rational points and Lang maps. Partially supported by NSF grant DMS-9503276.     

On a paper of Edmunds and Opic on limiting interpolation of compact operators between spaces

We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of spaces.