For sufficiently large k and l, all zeros of E_k² + E_{2k}, E_k³ + E_{3k}, and E_k E_l + E_{k+l} in the fundamental domain lie on the arc A = {e^{iθ} : π/2 ≤ θ ≤ 2π/3}.
Zeros of weakly holomorphic modular forms of levels 2 and 3
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abstract
Let $M_k^\sharp(N)$ be the space of weakly holomorphic modular forms for $\Gamma_0(N)$ that are holomorphic at all cusps except possibly at $\infty$. We study a canonical basis for $M_k^\sharp(2)$ and $M_k^\sharp(3)$ and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.
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math.NT 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Zeros of certain combinations of Eisenstein series of weight 2k, 3k, and k + l
For sufficiently large k and l, all zeros of E_k² + E_{2k}, E_k³ + E_{3k}, and E_k E_l + E_{k+l} in the fundamental domain lie on the arc A = {e^{iθ} : π/2 ≤ θ ≤ 2π/3}.