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Zeros of modular forms of half integral weight [PDF]
Research in Number Theory, 2016 We study canonical bases for spaces of weakly holomorphic modular forms of level 4 and weights in $\mathbb{Z}+\frac{1}{2}$ and show that almost all modular forms in these bases have the property that many of their zeros in a fundamental domain for ...
Folsom, Amanda, Jenkins, Paul
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Sign of Fourier coefficients of modular forms of half integral weight [PDF]
Mathematika, 2015 International audienceWe establish lower bounds for (i) the numbers of positive and negative terms and (ii) the number of sign changes in the sequence of Fourier coefficients at squarefree integers of a half-integral weight modular Hecke ...
Lau, Yuk-Kam, Royer, Emmanuel, Wu, Jie
core +9 more sources
Bounds on sup-norms of half-integral weight modular forms [PDF]
Acta Arithmetica, 2014 Bounding sup-norms of modular forms in terms of the level has been the focus of much recent study. In this work the sup norm of a half integral weight cusp form is bounded in terms of the level.Comment: 11 pages.
Kiral, Eren Mehmet
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Sign changes of coefficients of half integral weight modular forms [PDF]
, 2007 For a half integral weight modular form $f$ we study the signs of the Fourier coefficients $a(n)$. If $f$ is a Hecke eigenform of level $ N$ with real Nebentypus character, and $t$ is a fixed square-free positive integer with $a(t)\neq 0$, we show that ...
Bruinier, Jan Hendrik, Kohnen, Winfried
core +3 more sources
Fast computation of half-integral weight modular forms
Rocky Mountain Journal of Mathematics, 2022 To study statistical properties of modular forms, including for instance Sato-Tate like problems, it is essential to have a large number of Fourier coefficients. In this article, we exhibit three bases for the space of modular forms of any half-integral weight and level 4, which have the property that many coefficients can be computed (relatively ...
Inam, Ilker, Wiese, Gabor
openaire +5 more sources
Modular forms of half-integral weight on Γ0(4) with few nonvanishing coefficients modulo ℓ
Open Mathematics, 2022 Let kk be a nonnegative integer. Let KK be a number field and OK{{\mathcal{O}}}_{K} be the ring of integers of KK. Let ℓ≥5\ell \ge 5 be a prime and vv be a prime ideal of OK{{\mathcal{O}}}_{K} over ℓ\ell . Let ff be a modular form of weight k+12k+\frac{1}
Choi Dohoon, Lee Youngmin
doaj +1 more source
Period functions of half-integral weight modular forms [PDF]
Journal de théorie des nombres de Bordeaux, 2015 In this paper, we study the Eichler cohomology associated with half-integral weight cusp forms using the Dedekind eta function η(z) and the theta function θ(z). We prove that η-multiplication (resp. θ-multiplication) gives an isomorphism between the space of cusp forms of a half-integral weight and the cohomology group associated with the space η𝒫 ...
Choi, Dohoon, Lim, Subong, Raji, Wissam
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Periodicities for Taylor coefficients of half-integral weight modular forms [PDF]
Pacific Journal of Mathematics, 2020 Congruences of Fourier coefficients of modular forms have long been an object of central study. By comparison, the arithmetic of other expansions of modular forms, in particular Taylor expansions around points in the upper-half plane, has been much less studied.
Guerzhoy, P., Mertens, M., Rolen, L.
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Bounds for twisted symmetric square L-functions via half-integral weight periods
Forum of Mathematics, Sigma, 2020 We establish the first moment bound $$\begin{align*}\sum_{\varphi} L(\varphi \otimes \varphi \otimes \Psi, \tfrac{1}{2}) \ll_\varepsilon p^{5/4+\varepsilon} \end{align*}$$ for triple product L-functions, where $\Psi $ is a fixed Hecke ...
Paul D. Nelson
doaj +1 more source
Shintani lifts and fractional derivatives for harmonic weak Maass forms [PDF]
, 2014 In this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms.
Bringmann, Kathrin +2 more
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