A note on a result of Erdös, Sárkőzy and Sós
A note on a theorem of Hardy and Littlewood
A note on arithmetic Diophantine series
We consider an asymptotic analysis for series related to the work of Hardy and Littlewood (1923) on Diophantine approximation, as well as Davenport. In particular, we expand on ideas from some previous work on arithmetic series and the RH. To accomplish this, Mellin inversion is applied to certain infinite series over arithmetic functions to apply Cauchy's residue theorem, and then the remainder of terms is estimated according to the assumption of the RH. In the last section, we use simple properties...
A note on arithmetic progressions on elliptic curves.
A note on arithmetic progressions on quartic elliptic curves.
A note on Artin's conjecture in algebraic number fields.
A note on automorphic forms.
A note on average behaviour of the Fourier coefficients of th symmetric power -function over certain sparse sequence of positive integers
Let be a given integer. Let be the set of all normalized primitive holomorphic cusp forms of even integral weight for the full modulo group . For , denote by the th normalized Fourier coefficient of th symmetric power -function () attached to . We are interested in the average behaviour of the sum where is sufficiently large, which improves the recent work of A. Sharma and A. Sankaranarayanan (2023).
A note on sets.
A note on basic Iwasawa ?-invariants of imaginary quadratic fields.
A note on basic Iwasawa λ-invariants of imaginary quadratic fields and congruence of modular forms
A Note on Bernoulli numbers and polynomials.
A note on Boolean lattices and Farey sequences.
A note on Boolean lattices and Farey sequences. II.
A note on Catalan's equation
A note on certain semigroups of algebraic numbers
The cross number κ(a) can be defined for any element a of a Krull monoid. The property κ(a) = 1 is important in the study of algebraic numbers with factorizations of distinct lengths. The arithmetic meaning of the weaker property, κ(a) ∈ ℤ, is still unknown, but it does define a semigroup which may be interesting in its own right. This paper studies some arithmetic(divisor theory) and analytic(distribution of elements with a given norm) properties of that semigroup and a related semigroup of ideals....
A note on character sums over finite fields.
A note on circular distributions
A note on circular units in -extensions
In this note we consider projective limits of Sinnott and Washington groups of circular units in the cyclotomic -extension of an abelian field. A concrete example is given to show that these two limits do not coincide in general.
A note on class number 1 criteria for totally real algebraic number fields