A note on the Hasse principle
A note on the Hasse principle. Addenda
A note on the Hausdorff-Besicovitch dimension of systems of linear forms
A note on the Hermite–Rankin constant
We generalize Poor and Yuen’s inequality to the Hermite–Rankin constant and the Bergé–Martinet constant . Moreover, we determine explicit values of some low- dimensional Hermite–Rankin and Bergé–Martinet constants by applying Rankin’s inequality and some inequalities proven by Bergé and Martinet to explicit values of , and ().
A Note on the Hurwitz Zeta Function
A note on the ideal class group of the cyclotomic ℤₚ-extension of a totally real number field
A note on the integer solutions ofhyperelliptic equations
A note on the large sieve
A note on the least prime in an arithmetic progression with a prime difference
A note on the limit points associated withthe generalized abc-conjecture for ℤ[t]
A note on the lonely runner conjecture.
A note on the mean value of the general Kloosterman sums
The main purpose of this paper is to use the analytic method to study the calculating problem of the general Kloosterman sums, and give an exact calculating formula for it.
A note on the modified -Bernstein polynomials.
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.