On Kaneko congruences
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2012
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University of Hawaii at Manoa
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Abstract
We present a proof of certain congruences modulo powers of an odd prime for the coefficients of a series produced by repeated application of U -operator to a certain weakly holomorphic modular form. This kind of congruences were first observed by Kaneko as a result of numerical experiments, and later proved in a different (but similar) case by Guerzhoy [6]. It is interesting to note that, in our case, the congruences become different, both experimentally and theoretically, depending on whether the prime is congruent to 1 or 3 modulo 4.
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Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2012
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20 pages
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