The Lazard formal group, universal congruences and special values of zeta functions
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2015
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Amer Mathematical Soc
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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 [31]-[33]. 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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© Amer Mathematical Soc.
The author is indebted to the unknown referee for many useful observations, which improved the quality of the paper. The author wishes to heartily thank Professor D. Zagier for interest in the work and for correcting an incorrect statement in an early version of the paper. The author is also grateful to Professor A. Granville for suggesting the cited Problem and to Professor R. A. Leo for many interesting and helpful discussions.
Part of this research work was carried out in the Centro di ricerche matematiche Ennio De Giorgi, Scuola Normale Superiore, Pisa, and the author kindly thanks this institution for its hospitality.
The support from the research project FIS2011–22566, Ministerio de Ciencia e Innovación, Spain is gratefully acknowledged.