• East Asian mathematical journal
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• 제31권5호
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• pp.659-665
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• 2015

Combining and specializing some known results, we establish six identities which depict six modular relations for the Roger-Ramanujan type identities and two equivalent representations for Jacobian identity expressed in terms of combinatorial partition identities and Ramanujan-Selberg continued fraction. Two q-product identities are also considered.

• 충청수학회지
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• 제24권3호
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• pp.481-502
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• 2011

B. C. Berndt [4, 5] evaluated several classes of infinite series and established many relations between various infinite series. In this paper, continuing his work, we derive new relations between infinite series.

• 대한수학회보
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• 제46권2호
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• pp.229-234
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• 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 ${GL_2}(\mathbb{F}_q[T])$.

• 대한수학회보
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• 제52권1호
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• pp.263-273
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• 2015

We derive modular equations of degree 2 to establish explicit relations for the parameterizations for the theta functions ${\varphi}$ and ${\psi}$. We then find specific values of the parameterizations to evaluate some new values of the modular j-invariant in terms of $J_n$.

• 대한수학회지
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• 제51권2호
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• pp.225-238
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• 2014

We apply modular function theory to find the relation among t-core partitions. By using the generators of function field corresponding to a certain modular group, we reprove the identities in [1] because their relations are linear for t = 3 or 5.

• 충청수학회지
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• 제35권4호
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• pp.277-295
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• 2022

The author proved a modular transformation formula for a function related to generalized non-holomorphic Eisenstein series and, using this formula, established a lot of infinite series identities. In this paper, we find more generalized series relations which contain the author's previous work.

• 충청수학회지
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• 제30권2호
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• pp.183-200
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• 2017

Zagier lift gives a relation between weakly holomorphic modular functions and weakly holomorphic modular forms of weight 3/2. Duke and Jenkins extended Zagier-lifts for weakly holomorphic modular forms of negative-integral weights and recently Bringmann, Guerzhoy and Kane extended them further to certain harmonic weak Maass forms of negative-integral weights. New Zagier-lifts for harmonic weak Maass forms and their relation with Bringmann-Guerzhoy-Kane's lifts were discussed earlier. In this paper, we give explicit relations between the two different lifts via direct computation.

• 대한수학회보
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• 제50권4호
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• pp.1315-1328
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• 2013

We first derive several modular equations of degree 5 and present their concise proofs based on algebraic computations. We then establish explicit relations and formulas for some parameterizations for the theta functions ${\varphi}$ and ${\psi}$ by using the derived modular equations. In addition, we find specific values of the parameterizations and evaluate some numerical values of the Rogers-Ramanujan continued fraction.

• 대한수학회보
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• 제50권4호
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• pp.1221-1233
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• 2013

We first derive some modular equations of degrees 3 and 9 and present their concise proofs based on algebraic computations. We then use these modular equations to establish explicit relations and formulas for the parameterizations for the theta functions ${\varphi}$ and ${\psi}$ In addition, we find specific values of the parameterizations to evaluate some numerical values of the cubic continued fraction.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.525-535
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• 2016

We define a fuzzy lattice as a fuzzy relation, prove the distributive inequalities and the modular inequality of fuzzy lattices, and show that the fuzzy totally ordered set is a distributive fuzzy lattice and that the distributive fuzzy lattice is modular.