Functional equations for double series of Euler type with coefficients

We prove two types of functional equations for double series of Euler type with complex coefficients. The first one is a generalization of the functional equation for the Euler double zeta-function, proved in a former work of the second-named author. The second one is more specific, which is proved...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2016-04, Vol.292, p.529-557
Main Authors: Choie, YoungJu, Matsumoto, Kohji
Format: Article
Language:English
Subjects:
Confluent hypergeometric function
Double zeta function
Functional equation
Iterated integrals of modular forms
Modular relation
Modular symbol
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Summary:We prove two types of functional equations for double series of Euler type with complex coefficients. The first one is a generalization of the functional equation for the Euler double zeta-function, proved in a former work of the second-named author. The second one is more specific, which is proved when the coefficients are Fourier coefficients of cusp forms and the modular relation is essentially used in the course of the proof. As a consequence of functional equation we are able to determine trivial zero divisors.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2016.01.016