On the non-quadraticity of values of the q-exponential function and related q-series
On the non-torsion elements in the algebraic K-theory of rings of integers.
On the non-triviality of the basic Iwasawa λ-invariant for an infinitude of imaginary quadratic fields
On the Non-Vanishing of Certain Poincaré Series.
On the nonvanishing of Fermat quotients (mod p).
On the normality of arithmetical constants.
On the not integrally closed subrings of the ring of the Thetanullwerte. II.
On the nth Powers of the Primitive Nth roots of Unity
On the number of Abelian groups of a given number.
On the number of Abelian groups of a given order
On the number of abelian groups of a given order
On the number of abelian groups of a given order (supplement)
1. Introduction. The aim of this paper is to supply a still better result for the problem considered in [2]. Let A(x) denote the number of distinct abelian groups (up to isomorphism) of orders not exceeding x. We shall prove Theorem 1. For any ε > 0, , where C₁, C₂ and C₃ are constants given on page 261 of [2]. Note that 50/199=0.25125..., thus improving our previous exponent 40/159=0.25157... obtained in [2]. To prove Theorem 1, we shall proceed along the line of approach presented in [2]....
On the number of Arnoux-Rauzy words
On the number of binary signed digit representations of a given weight
Binary signed digit representations (BSDR’s) of integers have been studied since the 1950’s. Their study was originally motivated by multiplication and division algorithms for integers and later by arithmetics on elliptic curves. Our paper is motivated by differential cryptanalysis of hash functions. We give an upper bound for the number of BSDR’s of a given weight. Our result improves the upper bound on the number of BSDR’s with minimal weight stated by Grabner and Heuberger in On the number of...
On the Number of Convex Lattice Polytopes.
On the number of coprime integer pairs within a circle
On the number of distinct values of Euler's φ-function
On the number of elements with maximal order in the multiplicative group modulo n
On the number of elliptic curves with CM cover large algebraic fields
Elliptic curves with CM unveil a new phenomenon in the theory of large algebraic fields. Rather than drawing a line between and or and they give an example where the line goes beween and and another one where the line goes between and .
On the number of equivalence classes of binary forms of given degree and given discriminant