96 Normat 60:1, 96 (2012)

Summary in English

Ulf Persson, Dan Laksov 1940-

2013 (Swedish)

An obituary of a Swedish-Norwegian

mathematician.

Christer Kiselman, Pierre Lelong

1912-2011 (English)

Pierre Lelong was a pioneer in the sub-

ject of several complex variables Among

his most important contributions count

the class of plurisubharmonic functions

(with Oka), the so called Lelong num-

ber, and integration on analytic sets.

The article also discusses the connection

of Lelong to Sweden, and discusses his

advice and inﬂuence at the highest le-

vels of Government. He was a personal

friend of Pompidou. As to his words of

wisdom one may note that in his opi-

nion the highest accolade a mathemati-

cian can get is that his work becomes

so familiar to his colleagues that they

consider it trivial.

Juliusz Brzezinski Hilberts Tionde

Problem och Büchisekvenser (Swedish)

Hilberts tenth problem has as is well-

known a negative answer which can be

given a positive form. One can write

down an explicit polynomial in sever-

al variables for which one cannot deci-

de in a ﬁnite number of steps whether

it has an integral solution. The pro-

blem is that the polynomial is compli-

cated and hardly transparent. Trying

to ﬁnd a conceptually simpler examp-

le Büchi studied sequences of integers

whose squares have the second diﬀeren-

ce equal to 2. There is a trivial solu-

tion, namely the consecutive integers,

and the conjecture is that any such se-

quence of length at least ﬁve is a subse-

quence of the trivial. Even if one allows

rational numbers in the sequence and do

not ﬁx the particular value of the con-

stant second diﬀerence, the lengths of

non-trivial sequences are severely limi-

ted. The problem has intriguing connec-

tions to geometry, which are exploited

in constructing explicit examples. Furt-

hermore p oss ible generalizations of Hil-

bert’s tenth problem are discussed, and

in an appendix there is an explana-

tion of the connection of those so called

Büchi sequences to values of quadratic

polynomials in consecutive integers.

Haakon Waadeland Ataleabouttails

-tailsastoolstailsastoys(English)

A continued fraction can be written

as a sum of an approximating fraction

(terminating the process at a ﬁnite sta-

ge) and the inﬁnite tail, which typically

is very small. This article is a playful

variation on the theme of varying the

tail, and hence the approximating ones,

leading to faster convergence.

Haakon Waadeland Reﬂections on a

CF-expansion of 2+2

1

3

(English)

C =3+

1

3+

C

3+

C

3+

C

3+

...

has C +2+2

1

3

as a solution. This gives

rise to a recursive formula

C

0

=3,C

1

=3+

1

3

and generally

C

n

=3+

1

3+C

n≠2

(C

n≠1

≠ 3)

with rapid convergence. Variations are

discussed.