Dohoon Choi

In his last letter to Hardy, Ramanujan introduced mock theta functions. For each of his examples $f(q)$, Ramanujan claimed that there is a collection $\{ G_j\}$ of modular forms such that for each root of unity $\zeta$, there is a $j$ such that \[ \lim _{q \to \zeta }(f(q) - G_j(q)) = O(1).\] Moreover, Ramanujan claimed that this collection must have size larger than $1$. In his 2001 PhD thesis, Zwegers showed that the mock theta functions are the holomorphic parts of harmonic weak Maass forms.

Suppose that $f$ is an elliptic modular form with integral coefficients. Sturm obtained bounds for a nonnegative integer $n$ such that every Fourier coefficient of $f$ vanishes modulo a prime $p$ if the first $n$ Fourier coefficients of $f$ are zero modul

We employ recent results on Jacobi forms to investigate congruences and filtrations of Siegel modular forms of degree <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>2</mml:mn> </mml:math> . In particular, we determine when an analog of Atkin’s <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -operator applied to a Siegel modular form of degree <mml:math xmlns

Zagier introduced special bases for weakly holomorphic modular forms to give the new proof of Borcherds’ theorem on the infinite product expansions of integer weight modular forms on $\mathrm {SL}_2(\mathbb {Z})$ with a Heegner divisor. These good bases appear in pairs, and they satisfy a striking duality, which is now called Zagier duality. After the result of Zagier, this type of duality was studied broadly in various viewpoints, including the theory of a mock modular form. In this paper, we

Let $Γ$ be a finitely generated Fuchsian group of the first kind which has at least one parabolic class. Eichler introduced a cohomology theory for Fuchsian groups, called as "Eichler cohomology theory", and established the $\CC$-linear isomorphism from the direct sum of two spaces of cusp forms on $Γ$ with the same integral weight to the Eichler cohomology group of $Γ$. After the results of Eichler, the Eichler cohomology theory was generalized in various ways. For example, these results were g

In this paper, a slot antenna is proposed to achieve both harmonic suppression and wide bandwidth. To obtain these results, a T-shaped microstrip-line-fed slot antenna and U-shaped conductor line connected with the ground plane are applied. At the fundamental and harmonic frequencies, return loss and radiation characteristics are measured and compared with those of the conventional slot antenna. For the proposed antenna, the 10-dB return loss bandwidth could reach 1220 MHz (1730-2950 MHz), which