48 Normat 56:1, 48 (2008)

Summary in English

Nils Baas and Christian Skau, Sel-

bergintervjuet I - Matematisk Oppvext

(Norwegian).

This is part one of four of an inter-

view with Atle Selberg (1917-2007) con-

ducted a couple of months before he

died. It treats his childhood and youth

up to his departure for the US after

the war. It is a mixture of private rem-

iniscences, mostly of interest to Nor-

wegians, and his mathematical awak-

ening. Selberg was the youngest child

in a family of ﬁve children, three of

which became professors of mathemat-

ics. His ﬁrst recorded mathematical dis-

covery was that squares diﬀered by the

odd numbers made at the age of seven

or so. At ﬁfteen he discovered a con-

nection between the integral

R

1

0

dx

x

x

and

the series

P

∞

n=1

1

n

n

which was also pub-

lished as a note, incidentally in Nor-

mat (1933). Early on he encountered

the works of Ramanujam and his ﬁrst

article (Über einige arithmetische Iden-

titäten) treated mock theta-functions

and was sent to Watson (of Whittaker

and W.) who, however, was very tardy.

For his preliminary work at the univer-

sity of Oslo in 1939 under Skolem he

considered modular forms represented

by Poincaré series. It turned out to be

extensive enough to have qualiﬁed as

a doctoral dissertation, but for that he

had other plans. But even before that

he had extended work on the partition

function done by Hardy and Ramanu-

jam only to discover that he had been

anticipated by Rademacher. It was a

big disappointment and he decided not

to publish it, although his results were

sharper.

He spent some time at Uppsala,

which had a better library than Oslo,

where he learned for the ﬁrst time of the

hyperbolic plane. In fact his geometrical

education had been spotty, and he had

encountered the trigonometric functions

for the ﬁrst time in his life in connection

with Eulers formulas! During the Ger-

man invasion of Norway he was drafted

into the military resistance, which, how-

ever, did not last long and permitted

him to return to mathematics, in which

he now started to focus on the Riemann

zetafunction. His improvement on the

estimates of Hardy and Littlewood were

so spectacular that when H. Bohr was

asked what had happened in European

mathematics during the war he simply

replied – Selberg.

Paul Papatzacos, Formler for π

fra femtenhundretallets Kerela (Norwe-

gian).

The Leibniz formula

π

4

= 1 −

1

3

+

1

5

−

1

7

. . . is of course well-known, and one of

the ﬁrst inﬁnite series for π which peo-

ple usually encounter. However, it was

known in India long before it was re-

discovered by Gregory and Leibniz. Its

convergence is very slow, but it can be

souped up by adding an appropriate rest

term, which was also known to the In-

dians in Kerala. How did they ﬁnd it?

By trial and error, or maybe by contin-

ued fractions? The latter gives an ele-

gant, but maybe anachronistic explana-

tion. Rewampings of the series as

π

4

=

7

9

+ 36

P

∞

m=1

1

((n

3

−n)(n−1)

2

+5)((n+1)

2

+5)

with n = 2m + 1 were known to them

already in the 16th century.