The Lazard formal group, universal congruences and special values of zeta functions
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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.References
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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
- © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 7015-7028
- MSC (2010): Primary 97Fxx; Secondary 57N65
- DOI: https://doi.org/10.1090/tran/6234
- MathSciNet review: 3378822