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Natural Boundaries II: Algebraic Groups

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1925)

In this chapter, we use the analysis of the previous section to prove that the zeta functions of the classical groups GO2l+1, GSp2l or GO+2l of types B l for l ≥ 2, C l for l ≥ 3 and D l for l ≥ 4 have natural boundaries. These results were announced in [18]. We recall the definition of the local factors and the formula in terms of the root system established in [36] and [21].

Keywords

  • Meromorphic Function
  • Zeta Function
  • Algebraic Group
  • Positive Root
  • Weyl Group

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© 2008 Springer-Verlag Berlin Heidelberg

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(2008). Natural Boundaries II: Algebraic Groups. In: Zeta Functions of Groups and Rings. Lecture Notes in Mathematics, vol 1925. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74776-5_6

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