期刊
ADVANCES IN MATHEMATICS
卷 292, 期 -, 页码 529-557出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2016.01.016
关键词
Iterated integrals of modular forms; Modular symbol; Double zeta function; Functional equation; Confluent hypergeometric function; Modular relation
类别
资金
- NRF [2015049582, 2013R1A2A2A01068676]
- JSPS [25287002]
- Grants-in-Aid for Scientific Research [16H02143, 16H06336, 25287002] Funding Source: KAKEN
- National Research Foundation of Korea [2013R1A2A2A01068676] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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. (C) 2016 Elsevier Inc. All rights reserved.
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