Kurt Girstmair

collaborators

6 papers

math.NT2026

The mean value of the digits of $1/ p$

Kurt Girstmair

Let $p \geq 3$ be a prime and $b \geq 2$ an integer such that $p$ does not divide $b$ . Then $1/ p$ has a periodic digit expansion with respect to the basis $b$ . The length $l$ of the pe…

math.NT2026

Mean values and variances of the digits of $1/ p$

Kurt Girstmair

Let $p \geq 3$ be a prime and $b \geq 2$ an integer such that $p$ does not divide $b$ . Then $1/ p$ has a periodic digit expansion with respect to the basis $b$ . The length $l$ of the pe…

math.NT2026

Digit frequencies and class numbers

Kurt Girstmair

Let $p > 3$ be a prime and $b \geq 2$ an integer such that $p$ does not divide $b$ . Then $1/ p$ has a periodic digit expansion with respect to the basis $b$ . The length $m$ of the perio…

math.NT2026

On the variance of the digits of $1/ p$

Kurt Girstmair

Let $p > 3$ be a prime and $b \geq 2$ an integer such that $p$ does not divide $b$ . Then $1/ p$ has a periodic digit expansion with respect to the basis $b$ . The length $q$ of the perio…

math.NT2025

On the decimal and octal digits of $1/ p$

Kurt Girstmair

Let $p$ be a prime $\equiv 3$ mod 4, $p > 3$ , and suppose that 10 has the order $(p - 1) /2$ mod p. Then $1/ p$ has a decimal period of length $(p - 1) /2$ . We express the frequency of each…

math.NT2025

Power residues, digit expansions and relative class numbers

Kurt Girstmair

This is a survey of a connection between the distribution of certain power residues modulo $p$ , $p$ a prime, and relative class numbers. The focus lies on quadratic residues and si…

The mean value of the digits of 1/p

Mean values and variances of the digits of 1/p

Digit frequencies and class numbers

On the variance of the digits of 1/p

On the decimal and octal digits of 1/p

Power residues, digit expansions and relative class numbers

The mean value of the digits of $1/ p$

Mean values and variances of the digits of $1/ p$

On the variance of the digits of $1/ p$

On the decimal and octal digits of $1/ p$