A multivariable Euler product of Igusa type and its applications

Nobushige Kurokawa, Hiroyuki Ochiai

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Knowing the number of solutions for a Diophantine equation is an important step to study various arithmetic problems. Igusa originated the study of Igusa zeta functions associated to local Diophantine problems. Multiplying all these local Igusa zeta functions we obtain the global version in the natural way. Unfortunately, investigations on global Igusa zeta functions are rare up to now. Reformulating the global Igusa zeta function via the number of morphisms between algebraic systems we discover a new aspect: the multivariable Euler product of Igusa type and its applications. A purpose of this paper is to encourage experts for further studies on global Igusa zeta functions by treating a simple interesting example.

Original languageEnglish
Pages (from-to)1919-1930
Number of pages12
JournalJournal of Number Theory
Volume129
Issue number8
DOIs
Publication statusPublished - Aug 1 2009
Externally publishedYes

Fingerprint

Euler Product
Riemann zeta function
Diophantine equation
Number of Solutions
Morphisms

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

A multivariable Euler product of Igusa type and its applications. / Kurokawa, Nobushige; Ochiai, Hiroyuki.

In: Journal of Number Theory, Vol. 129, No. 8, 01.08.2009, p. 1919-1930.

Research output: Contribution to journalArticle

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