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Dirichlet Series and Polynomial Euler Products

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1877)

In this chapter, we introduce a class of Dirichlet series satisfying several quite natural analytic axioms in addition with two arithmetic conditions, namely, a polynomial Euler product representation and some kind of prime number theorem. The elements of this class will be the main actors in the sequel; however, for some of the later results we do not need to assume all of these axioms. Further, we shall prove mean-value estimates for the Dirichlet series coe.cients of these L-functions as well as asymptotic mean-square formulae on vertical lines in the critical strip. These estimates will turn out to be rather useful in later chapters.

Keywords

  • Dirichlet Series
  • Absolute Convergence
  • Local Root
  • Euler Product
  • Prime Number Theorem

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© 2007 Springer-Verlag Berlin Heidelberg

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(2007). Dirichlet Series and Polynomial Euler Products. In: Value-Distribution of L-Functions. Lecture Notes in Mathematics, vol 1877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44822-8_2

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