CONVERGENCE OF DIRICHLET SERIES AND EULER PRODUCTS
2017 ◽
Vol 38
(2)
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pp. 153
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The first part of this paper deals with Dirichlet series, and convergence theorems are proved that strengthen the classical convergence theorem as found e.g. in Serre’s “A Course in Arithmetic.” The second part deals with Euler-type products. A convergence theorem is proved giving sufficient conditions for such products to converge in the half-plane having real part greater than 1/2. Numerical evidence is also presented that suggests that the Euler products corresponding to Dirichlet L-functions L(s, χ), where χ is a primitive Dirichlet character, converge in this half-plane.
1984 ◽
Vol 25
(1)
◽
pp. 107-119
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Keyword(s):
2016 ◽
Vol 103
(2)
◽
pp. 231-249
Keyword(s):
Keyword(s):