88 Normat 51:2, 88 (2003)
Summary in English
Ernst E. Scheufens, Sum and inte-
gral representations for (3) and related
constants. (Danish.) After some histor-
ical remarks about (3) a new summa-
tion representation of (3) and related
constants is found using a Fourier series
method. The summation representation
is shown to be equivalent to some known
integral representations.
Knut Meen, Weibull in the drawer.
(Norwegian.) The article studies the
probability distribution for the number
of drawings necessary to obtain one pair,
when the drawings are done without
replacement from an urn c ontaining n
pairs (Feller’s shoe problem.) An algo-
rithm for computing the exact probabil-
ity distribution is given, and an approx-
imate formula, applicable for both small
and large values of n, is presented. When
n a Weibull distribution reveals it-
self. How well the approximate formula
and the Weibull distribution behaves is
demonstrated with some numerical ex-
amples.
Martin Raussen, A second look at
normal curvature. (English.)
Gert Almkvist, Strings in moonshine
II. (Swedish.) In this second part (the
first part appeared in the previous is-
sue) the author finds a condition on
the coefficients of a 4
th
order differential
equation such that the formula for the
Yukawa coupling should be valid. Some
examples of higher order equations are
given where the mirror map has inte-
ger coefficients. In the appendix a cat-
alogue is given with all the known 4
th
order differential equations having inte-
ger mirror maps. It is remarkable that in
all these 14 cases the n
d
’s of the Yukawa
coupling are also integers. All these ex-
amples have “Hodge index” h
1,1
=1.
Added in proof is one case of more
complicated 4
th
order equations (having
h
1,1
> 1). It looks as if there are at
least 14 such equations also having in-
teger mirror maps and n
d
.
Kent Holing, When does the quartic
equation have constructible roots? Ad-
ditional comment on the Galois group.
(Norwegian.) This is a f ollowup of a pa-
per by the author in the previous issue.
It discusses a method to calculate the
Galois group of a monic quartic equa-
tion with integral coefficients when the
equation is reducible over Z. It is shown
that the Galois group can then easily be
determined given only the number of in-
tegral roots and the discriminant of the
quartic equation. Together with the ear-
lier paper (which treated the irreducible
case of the quartic equation) this gives a
complete method to determine the Ga-
lois group of a general quartic equation
with rational coefficients, using condi-
tions easily given by the coefficients of
the equation.
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