On an identity between infinite series of arithmetic functions
On an improvement of a theorem of T. Nagell concerning the Diophantine equation Ax3 + By3 = C
On an inequality for additive arithmetic functions
On an inequality related to the Legendre totient function.
On an integer sequence related to a product of trigonometric functions, and its combinatorial relevance.
On an irreducibility theorem of I. Schur
On an isotropy criterion for quadratic forms over function fields of curves over non-dyadic complete discrete valuation rings
Harbater, Hartmann and Krashen obtained in 2015 a criterion for the existence of rational points on projective (or principal) homogeneous varieties for rational connected algebraic groups defined over function fields of normal curves over a complete discrete valuation ring in terms of completions of local rings at special points. This was obtained by a reduction via Artin approximation to a related patching problem solved by the same authors in 2009. In the special case of projective quadrics, we...
On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan
We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the -transform employed previously by Varshamov and Garakov (1969) as well as by Meyn (1990) for the synthesis of irreducible polynomials. While in the iterative procedure described by Kyuregyan the coefficients of the initial polynomial of the sequence have to satisfy certain hypotheses, in the...
On annihilators of the class group of an imaginary compositum of quadratic fields
On another sieve method and the numbers that are a sum of two hth powers: II.
On anti-elite prime numbers.
On approximate roots of a polynomial.
On approximation by Lüroth series
Let and be its sequence of Lüroth Series convergents. Define the approximation coefficients by . In [BBDK] the limiting distribution of the sequence was obtained for a.e. using the natural extension of the ergodic system underlying the Lüroth Series expansion. Here we show that this can be done without the natural extension. In fact we will prove that for each is already distributed according to the limiting distribution. Using the natural extension we will study the distribution for...
On approximation of real numbers by real algebraic numbers
On approximation to real numbers by algebraic numbers
On arbitrary products of eigenforms
We characterize all the cases in which products of arbitrary numbers of nearly holomorphic eigenforms and products of arbitrary numbers of quasimodular eigenforms for the full modular group SL₂(ℤ) are again eigenforms.
On arithmetic Fuchsian groups and their characterizations
This is a small survey paper about connections between the arithmetic and geometric properties in the case of arithmetic Fuchsian groups.
On arithmetic functions with congruence property
On arithmetic in Mordell-Weil groups
On arithmetic progressions having only few different prime factors in comparison with their length