Detchat Samart
Burapha University
26 Papers
40 Citations
Detchat Samart is an academic researcher from Burapha University. The author has contributed to research in topics: Mahler measure & Modular form. The author has an hindex of 6, co-authored 23 publications. Previous affiliations of Detchat Samart include Texas A&M University & Université de Montréal.
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Papers
Three-variable Mahler measures and special values of modular and Dirichlet $L$-series
TL;DR: In this article, it was shown that the Mahler measures of the Laurent polynomials can also be expressed in terms of logarithms and $_5F_4$-hypergeometric series.
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Feynman integrals and critical modular $L$-values
TL;DR: In this paper, it was shown that Broadhurst's conjecture holds up to a rational factor and that the Feynman integral associated to the polynomial corresponding to the corresponding to $t = 1$ in the one-parameter family is expressible in terms of $L(f,2), where f is a cusp form of weight $3$ and level $15$.
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Mahler Measures as Linear Combinations of $L$-values of Multiple Modular Forms
TL;DR: In this article, the authors studied the Mahler measures of certain families of Laurent polynomials in two and three variables, and showed that the number of modular values appearing in the formulas significantly depends on the shape of the algebraic value of the parameter chosen for each polynomial.
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Further explorations of Boyd's conjectures and a conductor 21 elliptic curve
TL;DR: In this paper, it was shown that the (logarithmic) Mahler measure m(P ) of P (x, y) = x + 1/x + y + 1 /y + 3 is equal to the L-value 2L′(E, 0) attached to the elliptic curve E : P = 0 of conductor 21, due to the Mellit-Brunault formula for the regulator of modular units.
Mahler measures as linear combinations of $L$-values of multiple modular forms
TL;DR: In this article, the authors studied the Mahler measures of certain families of Laurent polynomials in two and three variables, and showed that the number of modular $L$-values appearing in the formulas significantly depends on the shape of the algebraic value of the parameter chosen for each polynomial.
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