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On Generalized Dirichlet Series
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Dirichlet series, or, series of the form D(A, s) = ∞ i=1 a i i s are central objects in complex analysis and analytic number theory. This paper seeks to generalize them by introducing & studying new types of Dirichlet series-quaternionic Dirichlet series, and lattice Dirichlet series. That is, Dirichlet series over quaternions, and, various types of Dirichlet series over lattices.
Title: On Generalized Dirichlet Series
Description:
Dirichlet series, or, series of the form D(A, s) = ∞ i=1 a i i s are central objects in complex analysis and analytic number theory.
This paper seeks to generalize them by introducing & studying new types of Dirichlet series-quaternionic Dirichlet series, and lattice Dirichlet series.
That is, Dirichlet series over quaternions, and, various types of Dirichlet series over lattices.
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