Special values of zeta functions and areas of triangles

Snapshots of modern mathematics from 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 MordellTornheim zeta function using the Stern—Brocot tree. This example allows a geometric interpretation related to current research.

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Mathematical subjects

Algebra and Number Theory

Connections to other fields

Physics

Author(s)

Jürg Kramer, Anna-Maria Pippich
Senior Editor:
Carla Cederbaum
Junior Editor:
Sophia Jahns

License

DOI (Digital Object Identifier)

10.14760/SNAP-2015-010-EN

PDF

snapshots: overview

Mathematical subjects

Algebra and Number Theory
Analysis
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Finance
Humanities and Social Sciences
Life Science
Physics
Reflections on Mathematics

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