Results 51 to 60 of about 230 (149)
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.
Guerzhoy, P +5 more
core +1 more source
Hecke grids and congruences for weakly holomorphic modular forms
, 2013 Let $U(p)$ denote the Atkin operator of prime index $p$. Honda and Kaneko proved infinite families of congruences of the form $f|U(p) \equiv 0 \pmod{p}$ for weakly holomorphic modular forms of low weight and level and primes $p$ in certain residue classes, and conjectured the existence of similar congruences modulo higher powers of $p$. Partial results
Ahlgren, Scott, Andersen, Nickolas
openaire +2 more sources
Solvability of invariant systems of differential equations on H2$\mathbb {H}^2$ and beyond
Mathematische Nachrichten, Volume 299, Issue 2, Page 456-479, February 2026.Abstract We show how the Fourier transform for distributional sections of vector bundles over symmetric spaces of non‐compact type G/K$G/K$ can be used for questions of solvability of systems of invariant differential equations in analogy to Hörmander's proof of the Ehrenpreis–Malgrange theorem.
Martin Olbrich, Guendalina Palmirotta
wiley +1 more source
Module structure of Weyl algebras
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract The seminal paper (Stafford, J. Lond. Math. Soc. (2) 18 (1978), no. 3, 429–442) was a major step forward in our understanding of Weyl algebras. Beginning with Serre's Theorem on free summands of projective modules and Bass' Stable Range Theorem in commutative algebra, we attempt to trace the origins of this work and explain how it led to ...
Gwyn Bellamy
wiley +1 more source
One‐level densities in families of Grössencharakters associated to CM elliptic curves
Mathematika, Volume 72, Issue 1, January 2026.Abstract We study the low‐lying zeros of a family of L$L$‐functions attached to the complex multiplication elliptic curve Ed:y2=x3−dx$E_d \;:\; y^2 = x^3 - dx$, for each odd and square‐free integer d$d$. Specifically, upon writing the L$L$‐function of Ed$E_d$ as L(s−12,ξd)$L(s-\frac{1}{2}, \xi _d)$ for the appropriate Grössencharakter ξd$\xi _d$ of ...
Chantal David, Lucile Devin, Ezra Waxman
wiley +1 more source
Model category structures on truncated multicomplexes for complex geometry
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 4163-4177, December 2025.Abstract To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to N$N$‐multicomplexes. We present a family of model category structures on the category of N$N$‐multicomplexes where the weak equivalences are the morphisms inducing a quasi‐isomorphism ...
Joana Cirici +2 more
wiley +1 more source
W‐algebras, Gaussian free fields, and g$\mathfrak {g}$‐Dotsenko–Fateev integrals
Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.Abstract Based on the intrinsic connection between Gaussian free fields and the Heisenberg vertex algebra, we study some aspects of the correspondence between probability theory and W$W$‐algebras. This is first achieved by providing a construction of the W$W$‐algebra associated to a complex simple Lie algebra g$\mathfrak {g}$ by means of Gaussian free ...
Baptiste Cerclé
wiley +1 more source
Divisibility properties for weakly holomorphic modular forms with sign vectors [PDF]
International Journal of Number Theory, 2016 In this paper, we prove some divisibility results for the Fourier coefficients of reduced modular forms with sign vectors. More precisely, we generalize a divisibility result of Siegel on constant terms when the weight [Formula: see text], which is related to the weight of Borcherds lifts when [Formula: see text].
openaire +2 more sources
Persistence of unknottedness of clean Lagrangian intersections
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract Let Q0$Q_0$ and Q1$Q_1$ be two Lagrangian spheres in a six‐dimensional symplectic manifold. Assume that Q0$Q_0$ and Q1$Q_1$ intersect cleanly along a circle that is unknotted in both Q0$Q_0$ and Q1$Q_1$. We prove that there is no nearby Hamiltonian isotopy of Q0$Q_0$ and Q1$Q_1$ to a pair of Lagrangian spheres meeting cleanly along a circle ...
Johan Asplund, Yin Li
wiley +1 more source
Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2014 AbstractWe prove that the coefficients of the mock theta functions \begin{eqnarray*} f(q) = \sum_{n=1}^{\infty} \frac{ q^{n^2}}{(1+q)^2 (1+q^2)^2 \cdots (1+q^n)^2 } \end{eqnarray*} and \begin{eqnarray*} \omega(q)=1+\sum_{n=1}^\infty \frac{q^{2n^2+2n}}{(1+q)^2(1+q^3)^2\cdots (1+q^{2n+1})^2} \end{eqnarray*} possess no linear congruences modulo 3.
Ahlgren, Scott, Kim, Byungchan
openaire +3 more sources