Generalisation of the Kummer congruences
Adelberg generalised Kummer's congruences to the universal Bernoulli numbers. We complete the work he started and give results for all primes. This enables us to obtain a new congruence for the divided <I>Bernoulli</I> <I>numbers. </I>We also produce conjectures based on...
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Swansea University
2002
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| Online Access: | http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.637465 |
| Summary: | Adelberg generalised Kummer's congruences to the universal Bernoulli numbers. We complete the work he started and give results for all primes. This enables us to obtain a new congruence for the divided <I>Bernoulli</I> <I>numbers. </I>We also produce conjectures based on computer evidence which open up areas for further research. Finally we apply our methods to the <I>universal Bernoulli-Hurwitz numbers </I>and prove similar results for them. |
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