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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The Lazard formal group, universal congruences and special values of zeta functions
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by Piergiulio Tempesta PDF
Trans. Amer. Math. Soc. 367 (2015), 7015-7028 Request permission

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
  • © 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