Related papers: Appendix to "Twisting of Siegel paramodular forms"
We attempt to generalize a congruence property of elliptic modular forms proved by Sturm to that of Haupttypus of Siegel modular forms of degree 2 with level. Namely, we give an explicit bound of Fourier coefficients required to determine…
The first part of the paper is a survey of recent results about the cohomology of $(\phi,\Gamma)$-modules and its applications to the theory of Selmer complexes. In the second part we formulate a version of the Main Conjecture for $p$-adic…
In this note we improve on the results of our earlier paper[BLGG12], proving a near-optimal theorem on the existence of ordinary lifts of a mod l Hilbert modular form for any odd prime l.
A corrigendum of a former result on semisimplicity of the category of integrable modules of a q-boson algebra is given with a counter example.
An emended and improved version of the present paper has been archived in math-ph/0505057, and a preliminary account of its content has been published in Phys.Rev.Lett. 92, 60601, (2004). Moreover, in order to prove the relevance of…
This paper is withdrawn. We found a mistake in Lemma 4.1
Given a generalization of Lebesgue decomposition we obtain an extension to the finitely additive setting of the theorems of Halmos and Savage and of Yan.
The goal of this paper is to improve existing bounds for Fourier coefficients of higher genus Siegel modular forms of small weight.
We construct irreducible modules for twisted toroidal Lie algebras and extended affine Lie algebras. This is done by combining the representation theory of untwisted toroidal algebras with the technique of thin coverings of modules. We…
We prove that there exist exactly eight Siegel modular forms with respect to the congruence subgroups of Hecke type of the paramodular groups of genus two vanishing precisely along the diagonal of the Siegel upper half-plane. This is a…
This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…
In this work we use the Rankin-Selberg method to obtain results on the analytic properties of the standard $L$-function attached to vector valued Siegel modular forms. In particular we provide a detailed description of its possible poles…
We show that Siegel modular forms of level \Gamma_0(p^m) are p-adic modular forms. Moreover we show that derivatives of such Siegel modular forms are p-adic. Parts of our results are also valid for vector-valued modular forms. In our…
We use the category of linear complexes of tilting modules for the BGG category O, associated with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by…
This is a companion article to my papers on Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebras gl(m|n) (much revised!) and q(n). The goal is to develop the general theory of tilting modules for Lie superalgebras,…
Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…
These supplementary notes in the ArXiv are a companion to our paper "Bocher contractions of conformally superintegrable Laplace equations" [arXiv:1512.09315]. They contain background material and the details of the extensive computations…
Boris Shoikhet noticed that the proof of lemma 1 in section 2.3 of math.QA/0504420 contains an error. In this note I give a correct proof of this lemma which was suggested to me by Dmitry Tamarkin. The correction does not change the results…
This was originally an appendix to our paper `Fourier expansions at cusps' [arXiv:1807.00391]. The purpose of this note is to give a proof of a theorem of Shimura on the action of $\mathrm{Aut}(\mathbb{C})$ on modular forms for $\Gamma(N)$…
This text is an appendix to our work "On the growth of Kronecker coefficients", arXiv:1607.02887. Here, we provide some complementary theorems, remarks, and calculations that for the sake of space are not going to appear into the final…