YoungJu Choie
Pohang University of Science and Technology · 数学
研究室紹介
Professor YoungJu Choie's research lab specializes in arithmetic and analytic number theory, with a strong focus on modular forms, L-functions, and their arithmetic properties. The lab investigates deep connections between modular forms, Hecke eigenforms, and special values of L-functions, particularly through the study of period polynomials, Fourier coefficients, and their p-adic properties. A central theme is the interplay between modular forms and number-theoretic conjectures such as the Riemann Hypothesis, as seen in Robin’s criterion and related inequalities. The lab also explores theta lifts and Jacobi forms arising from combinatorial objects like codes, linking number theory with algebraic combinatorics.
Research Overview
Research Output Trend
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Selected Papers
15Robin’s criterion states that the Riemann Hypothesis (RH) is true if and only if Robin’s inequality <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>:</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mo>∑</mml:mo> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>|</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:mi>d</mml:mi> <mml:mo><</mml:mo> <mml:msup> <mml:mi>e</mml:mi> <
Here, a classical observation of Siegel is generalized by determining all the linear relations among the initial Fourier coefficients of a modular form on SL2(Z). As a consequence, spaces Mk are identified, in which there are universal p-divisibility properties for certain p-power coefficients. As a corollary, let f(z)=∑n=1∞af(n)qn∈Sk∩OL[[q]] be a normalized Hecke eigenform (note that q:=e2πiz), and let k ≡ δ(k) (mod 12), where δ(k) ∈ {4, 6, 8, 10, 14}. Reproducing earlier results of Hatada
Let $f=\sum_{n>o} a(n)q^{n}, a(n)$ real, be an arbitrary nonzero cusp form of even integral weight $k\geq 2$ on $\Gamma_0(N),$ square free $N.$ We obtain an effective bound that the first sign change of $a(n)$ occurs.
In this correspondence, we construct theta series that are Jacobi forms, from the complete enumerator of Type II codes over Z/sub 2m/. Moreover, we construct a map from a certain invariant space to the space of Jacobi forms on the full modular group.