Special values of zeta functions and areas of triangles

Instantanés de recherche mathématique à Oberwolfach

Special values of zeta functions and areas of triangles

In this snapshot we give a glimpse of the interplay of special values of zeta functions and volumes of triangles. Special values of zeta functions and their generalizations arise in the computation of volumes of moduli spaces (for example of Abelian varieties) and their universal spaces. As a first example, we compute the special value of the Riemann zeta function at s=2 and give its interpretation as the volume of the moduli space of elliptic curves. As a second example, we calculate a special value of the Mordell—Tornheim zeta function using the Stern—Brocot tree. This example allows a geometric interpretation related to current research.

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Sujet mathématique

Algèbre et théorie des nombres

Liens avec d'autres domaines

Physique

Auteur(s)

Jürg Kramer, Anna-Maria Pippich

Licence

DOI

10.14760/SNAP-2015-010-EN

Télécharger PDF

2015-010-pippich-kramer.pdf

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Sujet mathématique

Algèbre et théorie des nombres
Analyse
Pédagogie et éducation
Mathématiques discrètes et fondements des mathématiques
Géométrie et Topologie
Calcul numérique et calcul scientifique
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