Relations among Ramanujan-type congruences II: Ramanujan-type congruences in half-integral weights
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Martin Raum
Abstract
We link Ramanujan-type congruences, which emerge abundantly in combinatorics, to the Galois- and geometric theory of modular forms. Specifically, we show that Ramanujan-type congruences are preserved by the action of the shallow Hecke algebra, and discover a dichotomy between congruences originating in Hecke eigenvalues and congruences on arithmetic progressions with cube-free periods. The latter provide congruences among algebraic parts of twisted central
Funding source: Vetenskapsrådet
Award Identifier / Grant number: 2015-04139
Award Identifier / Grant number: 2019-03551
Funding statement: The author was partially supported by Vetenskapsrådet Grants 2015-04139 and 2019-03551.
Acknowledgements
The author wishes to thank Scott Ahlgren, Olivia Beckwith, and Olav Richter for inspiring discussions and helpful comments. The author is also grateful to the referee for their helpful and exceptionally thorough report.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- The theta cycles for modular forms modulo prime powers
- Relations among Ramanujan-type congruences II: Ramanujan-type congruences in half-integral weights
- A unified approach to Gelfand and de Vries dualities
- The cardinality of orthogonal exponentials of planar self-affine measures with two-element digit set
- Categorically closed countable semigroups
- Symmetric skew braces and brace systems
- A new class of uncertainty principles for the k-Hankel wavelet transform
- Homogeneous ACM bundles on isotropic Grassmannians
- On the global L 2-boundedness of Fourier integral operators with rough amplitude and phase functions
- A local converse theorem for Archimedean GL(n)
- Fractional Bloom boundedness and compactness of commutators
- A Mikhlin-type multiplier theorem for the partial harmonic oscillator
- Rational pullbacks of toric foliations
- On fractional integrals generated by Radon transforms over paraboloids
Artikel in diesem Heft
- Frontmatter
- The theta cycles for modular forms modulo prime powers
- Relations among Ramanujan-type congruences II: Ramanujan-type congruences in half-integral weights
- A unified approach to Gelfand and de Vries dualities
- The cardinality of orthogonal exponentials of planar self-affine measures with two-element digit set
- Categorically closed countable semigroups
- Symmetric skew braces and brace systems
- A new class of uncertainty principles for the k-Hankel wavelet transform
- Homogeneous ACM bundles on isotropic Grassmannians
- On the global L 2-boundedness of Fourier integral operators with rough amplitude and phase functions
- A local converse theorem for Archimedean GL(n)
- Fractional Bloom boundedness and compactness of commutators
- A Mikhlin-type multiplier theorem for the partial harmonic oscillator
- Rational pullbacks of toric foliations
- On fractional integrals generated by Radon transforms over paraboloids
