• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.507-522
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• 2020

We complete the construction of the nonlift weight two cusp paramodular Hecke eigenforms for prime levels N < 600, which arise in conformance with the paramodular conjecture of Brumer and Kramer.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.969-983
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• 2024

For an integer ℓ ≥ 1, let ${\bar{B}}_{\ell}(n)$ denotes the number of ℓ-regular over partition pairs of n. For certain conditions of ℓ, we study the divisibility of ${\bar{B}}_{\ell}(n)$ and arithmetic properties for ${\bar{B}}_{\ell}(n)$. We further obtain infinite family of congruences modulo 2^t satisfied by ${\bar{B}}_3(n)$ employing a result of Ono and Taguchi (2005) on nilpotency of Hecke operators.