p-Adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight [PDF]
Israel Journal of Mathematics, 2010 From the authors' abstract: Serre obtained the \(p\)-adic limit of the integral Fourier coefficients of modular forms on \(\text{SL}_2(\mathbb Z)\) for \(p=2,3,5,7\). In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on \(\Gamma_0(4N)\) for \(N=1,2,4\).
Youngju Choie
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Analogues of the Bol operator for half-integral weight weakly holomorphic modular forms [PDF]
Proceedings of the American Mathematical Society, 2023 We define an analogue of the Bol operator on spaces of weakly holomorphic modular forms of half-integral weight. We establish its main properties and relation with other objects.
Diamantis, Nikolaos +2 more
core +10 more sources
Half-integral weight p-adic coupling of weakly holomorphic and holomorphic modular forms [PDF]
Research in Number Theory, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kathrin Bringmann +2 more
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Skew-holomorphic Jacobi forms of index 1 and Siegel modular forms of half-integral weight
Journal of Number Theory, 2004 It is well known that Kohnen's ``\(+\)''-space of elliptic modular forms of half-integral weights \(k-1/2\) is isomorphic to the space of holomorphic resp. skew-holomorphic Jacobi forms of index 1 whenenver \(k\) is even resp. odd. In this paper the author generalizes this result to higher degrees. The space of skew-holomorphic Jacobi forms of odd resp.
exaly +3 more sources
Scalar‐valued depth two Eichler–Shimura integrals of cusp forms
Transactions of the London Mathematical Society, 2023 Given cusp forms f and g of integral weight k⩾2, the depth two holomorphic iterated Eichler–Shimura integral If,g is defined by ∫τi∞f(z)(X−z)k−2Ig(z;Y)dz, where Ig is the Eichler integral of g and X,Y are formal variables.
Tobias Magnusson, Martin Raum
doaj +1 more source
Weakly holomorphic modular forms of half-integral weight with nonvanishing constant terms modulo ℓ [PDF]
Transactions of the American Mathematical Society, 2009 Let ℓ \ell be a prime and
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$p$-adic Limit of Weakly Holomorphic Modular Forms of Half Integral Weight
, 2007 Serre obtained the p-adic limit of the integral Fourier coefficient of modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on $Γ_{0}(4N)$ for $N=1,2,4$.
Choi, Dohoon, Choie, YoungJu
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Towards quantum hierarchy for the Gromov–Witten theory of elliptic curves
Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.Abstract We construct the quantum double ramification (DR) hierarchy associated with the Gromov–Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbers of the DR cycle, the Gromov–Witten classes of the elliptic curve, and the Hodge class λg−1$\lambda _{g-1}$, together with vanishing results for λg−2$\lambda ...
Paolo Rossi +2 more
wiley +1 more source
Cycle integrals and rational period functions for Γ0+(2) and Γ0+(3)
Open MathematicsFor p∈{2,3}p\in \left\{2,3\right\} and an even integer kk, let Wk−2−(p){W}_{k-2}^{-}\left(p) be the space of period polynomials of weight k−2k-2 on Γ0+(p){\Gamma }_{0}^{+}\left(p) with eigenvalue −1-1 under the Fricke involution.
Choi SoYoung +2 more
doaj +1 more source
Invariant splitting principles for the Lipshitz–Ozsváth–Thurston correspondence
Journal of Topology, Volume 19, Issue 3, September 2026.Abstract We prove that the Lipshitz–Ozsváth–Thurston correspondence between extended type D structures of knot complements and F[U,V]/(UV)$\mathbb{F}[U,V]/(\textit{UV})$ knot Floer complexes can be arranged so that ιK${\iota}_{K}$‐invariant splittings of knot Floer chain complexes correspond to ιS3∖K${\iota}_{{S}^{3}\setminus K}$‐invariant splittings ...
Gary Guth, Sungkyung Kang
wiley +1 more source