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From Fourier Analysis and Number Theory to Radon Transforms and Geometry pp 293–302Cite as

On the Honda - Kaneko Congruences

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Part of the book series: Developments in Mathematics ((DEVM,volume 28))

Abstract

Several years ago, Kaneko experimentally observed certain congruences for the Fourier coefficients of a weakly holomorphic modular form modulo powers of primes. Recently, Kaneko and Honda proved that a special case of these congruences, namely, the congruences modulo single primes. In this chapter, we consider this weakly holomorphic modular form in the framework of the theory of mock modular forms, and prove a limit version of these congruences.

The author is thankful to Simons Foundation collabration Grant for the support.

Mathematics Subject Classification (2010): 11F33

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Authors and Affiliations

  1. Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Honolulu, HI, 96822-2273, USA

    P. Guerzhoy

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  1. P. Guerzhoy
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Correspondence to P. Guerzhoy .

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Editors and Affiliations

  1. , Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Hershel M. Farkas

  2. , Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, 08544, New Jersey, USA

    Robert C. Gunning

  3. , Department of Mathematics, Temple University, Wachman Hall 608, Philadelphia, 19122, Pennsylvania, USA

    Marvin I. Knopp

  4. , Department of Mathematics, University of Michigan, Church St. 530, Ann Arbor, 48109, Michigan, USA

    B. A. Taylor

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In memory of Leon Ehrenpreis

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Guerzhoy, P. (2013). On the Honda - Kaneko Congruences. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_12

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