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The Lazard formal group, universal congruences and special values of zeta functions


Author: Piergiulio Tempesta
Journal: Trans. Amer. Math. Soc. 367 (2015), 7015-7028
MSC (2010): Primary 97Fxx; Secondary 57N65
DOI: https://doi.org/10.1090/tran/6234
Published electronically: July 8, 2015
MathSciNet review: 3378822
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Abstract: A connection between the theory of formal groups and arithmetic number theory is established. In particular, it is shown how to construct general Almkvist-Meurman-type congruences for the universal Bernoulli polynomials that are related with the Lazard universal formal group (based on earlier works of the author). Their role in the theory of $ L$-genera for multiplicative sequences is illustrated. As an application, sequences of integer numbers are constructed. New congruences are also obtained, useful to compute special values of a new class of Riemann-Hurwitz-type zeta functions.


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Piergiulio Tempesta
Affiliation: Departamento de Física Teórica II, Facultad de Físicas, Universidad Complutense, 28040 Madrid, Spain – and – Instituto de Ciencias Matemáticas, C/ Nicolás Cabrera, No 13–15, 28049 Madrid, Spain
Email: p.tempesta@fis.ucm.es, piergiulio.tempesta@icmat.es

DOI: https://doi.org/10.1090/tran/6234
Received by editor(s): June 4, 2012
Received by editor(s) in revised form: December 21, 2012, and July 2, 2013
Published electronically: July 8, 2015
Additional Notes: The support from the research project FIS2011–22566, Ministerio de Ciencia e Innovación, Spain is gratefully acknowledged
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.