On relations between units of normal algebraic number fields and their subfields
On relative integral bases for unramified extensions
0. Introduction. Since ℤ is a principal ideal domain, every finitely generated torsion-free ℤ-module has a finite ℤ-basis; in particular, any fractional ideal in a number field has an "integral basis". However, if K is an arbitrary number field the ring of integers, A, of K is a Dedekind domain but not necessarily a principal ideal domain. If L/K is a finite extension of number fields, then the fractional ideals of L are finitely generated and torsion-free (or, equivalently, finitely generated and...
On relatively prime sets.
On relatively prime subsets and supersets.
On repdigit polygonal numbers.
On repetitions in frequency blocks of a generalized Fibonacci sequence.
On representation of cyclotomic fields
On representation of r-th powers by subset sums
On representations of a number as a sum of three triangles
On representations of numbers by sums of squares and quadratic fields
On representations of the Weil group with bounded conductor.
On Representing Integers as Products of the p + 1.
On representing the multiple of a number by a quadratic form
On restricted m-ary partitions.
On restricted sumsets in abelian groups of odd order.
On resultant inequalities
On Riemann Sums and Lebesgue Integrals.
On Riemann's Zeta Function.
On Robin’s criterion for the Riemann hypothesis
Robin’s criterion states that the Riemann Hypothesis (RH) is true if and only if Robin’s inequality is satisfied for , where denotes the Euler(-Mascheroni) constant. We show by elementary methods that if does not satisfy Robin’s criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreover, that must be divisible by a fifth power . As consequence we obtain that RH holds true iff every natural number divisible by a fifth power...
On Rödseth's h-bases A... 0 ...1, a..., 2a..., ..., (k - 2)a..., a...