Results 41 to 50 of about 205 (137)

Algebraic de Rham theory for weakly holomorphic modular forms of level one [PDF]

Algebra & Number Theory, 2018
We establish an Eichler-Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted coefficients. This leads to formulae for the periods and quasi-periods of modular forms.
Brown, Francis, Hain, Richard
openaire   +4 more sources

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

Quadratic Chabauty for Atkin-Lehner quotients of modular curves via weakly holomorphic modular forms: Hodge Filtrations [PDF]

32 pages, comments ...
Isabel Rendell
openalex   +3 more sources

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, Muriel Livernet, Sarah Whitehouse   +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

L-Series for Vector-Valued Weakly Holomorphic Modular Forms and Converse Theorems [PDF]

Canadian Journal of Mathematics
Abstract We introduce the L-series of weakly holomorphic modular forms using Laplace transforms and give their functional equations. We then determine converse theorems for vector-valued harmonic weak Maass forms, Jacobi forms, and elliptic modular forms of half-integral weight in Kohnen plus space.
Subong Lim, Wissam Raji
openalex   +3 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

Weakly special threefolds and nondensity of rational points

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We verify part of a conjecture of Campana predicting that rational points on the weakly special nonspecial simply connected smooth projective threefolds constructed by Bogomolov–Tschinkel are not dense. To prove our result, we establish fundamental properties of moduli spaces of orbifold maps, and prove a dimension bound for such moduli spaces
Finn Bartsch, Ariyan Javanpeykar, Erwan Rousseau   +2 more
wiley   +1 more source

Holomorphic field theories and higher algebra

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.
Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley   +1 more source