• 대한수학회보
• /
• 제46권2호
• /
• pp.229-234
• /
• 2009

We find congruences for the t-expansion coefficients of a Drinfeld modular form for ${\Gamma}^+_0$(Q), where Q is a monic irreducible polynomial. As an application we obtain new congruence relations for the t-expansion coefficients of Drinfeld modular forms for ${GL_2}(\mathbb{F}_q[T])$.

• 충청수학회지
• /
• 제26권4호
• /
• pp.923-926
• /
• 2013

We find congruence properties on the coefficients of modular forms for ${\Gamma}^+_0(5)$ generated by ${\Gamma}_0(5)$ and a Fricke involution $\(_{5\;0}^{0\;-1}\)$.

• 대한수학회논문집
• /
• 제23권4호
• /
• pp.479-485
• /
• 2008

In this note, we study arithmetic properties for the exponents of modular forms on ${\Gamma}_0(p)$ for primes p. Our aim is to refine the result of [4] by using the geometric property of the modular curve of ${\Gamma}_0(p)$.

• Journal of applied mathematics & informatics
• /
• 제42권4호
• /
• pp.969-983
• /
• 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.

• 대한수학회지
• /
• 제60권5호
• /
• pp.1073-1085
• /
• 2023

A partition of n is called a t-core partition if none of its hook number is divisible by t. In 2019, Hirschhorn and Sellers [5] obtained a parity result for 3-core partition function a3(n). Motivated by this result, both the authors [8] recently proved that for a non-negative integer α, a3αm(n) is almost always divisible by an arbitrary power of 2 and 3 and at(n) is almost always divisible by an arbitrary power of pji, where j is a fixed positive integer and t = pa11pa22···pamm with primes pi ≥ 5. In this article, by using Hecke eigenform theory, we obtain infinite families of congruences and multiplicative identities for a2(n) and a13(n) modulo 2 which generalizes some results of Das [2].