A note on the multiple twisted Carlitz's type -Bernoulli polynomials.
A Note on the Normality of Unramified, Abelian Extensions of Quadratic Extensions.
A note on the number of -sum-free sets.
A note on the number of -Diophantine quadruples
Let be an -tuple of positive, pairwise distinct integers. If for all the prime divisors of come from the same fixed set , then we call the -tuple -Diophantine. In this note we estimate the number of -Diophantine quadruples in terms of .
A note on the number of solutions of the generalized Ramanujan-Nagell equation
A note on the number of solutions of the generalized Ramanujan-Nagell equation
Let be a positive integer, and let be an odd prime with . In this paper we use a result on the rational approximation of quadratic irrationals due to M. Bauer, M. A. Bennett: Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. Ramanujan J. 6 (2002), 209–270, give a better upper bound for , and also prove that if the equation has integer solutions , the least solution of the equation satisfies , and , where is an effectively computable constant...
A note on the number of zeros of polynomials in an annulus
Let p(z) be a polynomial of the form , . We discuss a sufficient condition for the existence of zeros of p(z) in an annulus z ∈ ℂ: 1 - c < |z| < 1 + c, where c > 0 is an absolute constant. This condition is a combination of Carleman’s formula and Jensen’s formula, which is a new approach in the study of zeros of polynomials.
A note on the -adic Galois representations attached to Hilbert modular forms.
A note on the -adic gamma function
A note on the paper "Reducibility of lacunary polynomials I"
A note on the parity of the sum-of-digits function.
A note on the postage stamp problem.
A note on the pp conjecture for sheaves of spaces of orderings
In this note we provide a direct and simple proof of a result previously obtained by Astier stating that the class of spaces of orderings for which the pp conjecture holds true is closed under sheaves over Boolean spaces.
A note on the pseudorandomness of the Liouville function
A note on the -binomial rational root theorem.
A note on the -Euler measures.
A note on the -Genocchi numbers and polynomials.
A note on the ramification of torsion points lying on curves of genus at least two
Let be a curve of genus defined over the fraction field of a complete discrete valuation ring with algebraically closed residue field. Suppose that and that the characteristic of the residue field is not . Suppose that the Jacobian has semi-stable reduction over . Embed in using a -rational point. We show that the coordinates of the torsion points lying on lie in the unique tamely ramified quadratic extension of the field generated over by the coordinates of the -torsion...
A note on the representability of quaternary quadratic forms as sums of squares of two linear forms
A note on the sequence of A. F. Horadam.