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
exaly +6 more sources
Skew-holomorphic Jacobi forms of index 1 and Siegel modular forms of half-integral weight [PDF]
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.
Hayashida, Shuichi, Shuichi Hayashida
exaly +4 more sources
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
exaly +5 more sources
Scalar‐valued depth two Eichler–Shimura integrals of cusp forms [PDF]
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 +4 more sources
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
openaire +1 more source
$p$-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
openaire +2 more sources
Abelian number fields with frobenian conditions
Mathematika, Volume 72, Issue 4, October 2026.Abstract We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular, we find an asymptotic for the number of abelian field extensions of a number field k$k$ whose conductor is the sum of two squares. We also discuss an application of the Brauer group of stacks to quadratic number fields.
Julie Tavernier
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
Fock space of local fields of the discrete GFF and its scaling limit bosonic CFT
Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.Abstract To connect conformal field theories (CFTs) to probabilistic lattice models, recent works of Hongler et al. and Adame‐Carrillo have introduced a novel definition of local fields of the lattice models. Local fields in this picture are probabilistically concrete: they are built from random variables in the model.
David Adame‐Carrillo +2 more
wiley +1 more source