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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On differential equations associated with Euler product expressions


Author: Ian Knowles
Journal: Trans. Amer. Math. Soc. 289 (1985), 545-573
MSC: Primary 11M06; Secondary 30B50, 30E25
MathSciNet review: 784003
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Abstract: A method is given by which one may associate (uniquely) certain differential equations with analytic functions defined by certain Euler product expressions. Some of the consequences of this construction include results relating the location of the zeros of the analytic functions to asymptotic properties of the solutions of the differential equations, as well as a differential equation characterization of those Dirichlet series with multiplicative coefficients.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0784003-X
PII: S 0002-9947(1985)0784003-X
Article copyright: © Copyright 1985 American Mathematical Society