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Transactions of the American Mathematical Society

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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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Additional Information

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

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.