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The average of the least primitive root modulo $p^{2}$

D. Burgess — 1971

Acta Arithmetica

On a conjecture of Norton

D. Burgess — 1975

Acta Arithmetica

The N*-Metric Completion of Regular Rings.

Walter D. Burgess; David E. Handelman — 1982

Mathematische Annalen

Order completions of semiprime rings

Walter D. Burgess; Robert M. Raphael — 1981

Czechoslovak Mathematical Journal

On extending $C^{k}$ functions from an open set to $ℝ$ with applications

Walter D. Burgess; Robert M. Raphael — 2023

Czechoslovak Mathematical Journal

For $k \in ℕ \cup {\infty}$ and $U$ open in $ℝ$ , let $C^{k} (U)$ be the ring of real valued functions on $U$ with the first $k$ derivatives continuous. It is shown that for $f \in C^{k} (U)$ there is $g \in C^{\infty} (ℝ)$ with $U \subseteq coz g$ and $h \in C^{k} (ℝ)$ with ${f g |}_{U} {= h |}_{U}$ . The function $f$ and its $k$ derivatives are not assumed to be bounded on $U$ . The function $g$ is constructed using splines based on the Mollifier function. Some consequences about the ring $C^{k} (ℝ)$ are deduced from this, in particular that $Q_{cl} (C^{k} (ℝ)) = Q (C^{k} (ℝ))$ .

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Currently displaying 1 – 8 of 8

The average of the least primitive root modulo $p^{2}$

On a conjecture of Norton

The N*-Metric Completion of Regular Rings.

Order completions of semiprime rings

On extending $C^{k}$ functions from an open set to $ℝ$ with applications

On the average of character sums for a group of characters

A note on block triangular presentations of rings and finitistic dimension

Ring epimorphisms and $C (X)$ .