Related papers: Product formulas for modular forms on O(2,n) (afte…
This is the second part in a series of papers presenting a theory of tensor products for module categories for a vertex operator algebra. In Part I (hep-th/9309076), the notions of $P(z)$- and $Q(z)$-tensor product of two modules for a…
A simple application of the semipositivity.
We provide a construction of the multiplicative Borcherds lift for unitary groups U(1,m), which takes weakly holomorphic elliptic modular forms and lifts them to meromorphic automorphic forms having infinite product expansions and taking…
In this note we show that certain meromorphic orthogonal modular forms are magnetic, i.e.\ their Fourier coefficients satisfy special divisibility criteria. These meromorphic orthogonal modular forms are counterparts to the orthogonal cusp…
We discuss a product formula for $F$-polynomials in cluster algebras, and provide two proofs. One proof is inductive and uses only the mutation rule for $F$-polynomials. The other is based on the Fock-Goncharov decomposition of mutations.…
In this paper, we mainly characterize the structure of product bases of the complex vector space $\mathbb{C}^{2}\bigotimes\mathbb{C}^{n}$. It gives an answer to the conjecture in case of $d=2n$ proposed by McNulty et al in 2016. As the…
An extension of Chernoff's product formula for one-parameter functions taking values in the space of bounded linear operators on a Banach space is given. Essentially, the $n$-th one-parameter function in the product formula is mapped by the…
The purpose of this article is to show that Theorems 2.2-2.5 from [1] apply to the product of random matrices considered by Grama, Le Page, and Peign\'e [2]. This allows us, in particular, to emphasize the general nature of the formulation…
We use Borcherds products and their restrictions to Hirzebruch-Zagier curves to determine generators and relations for the graded rings of Hilbert modular forms for the fields $\mathbb{Q}(\sqrt{29})$ and $\mathbb{Q}(\sqrt{37})$. These seem…
We establish a new converse theorem for Borcherds products. Moreover, the injectivity of the Kudla-Millson theta lift is demonstrated in the O$(n,2)$ case in greater generality than is currently available in the literature. Both results are…
We define evaluation forms associated to objects in a module subcategory of Ext-symmetry generated by finitely many simple modules over a path algebra with relations and prove a multiplication formula for the product of two evaluation…
We consider multiplication properties of elements in weighted Fourier Lebesgue and modulation spaces. Especially we extend some results by Pilipovic, Teofanov and Toft (2010).
We show (under some hypothesis in small dimensions) that the analytic degree of the divisor of a modular form on the orthogonal group O(2,p) is determined by its weight. Moreover, we prove that certain integrals, occurring in Arakelov…
We present an algorithm to compute all Borcherds product paramodular cusp forms of a specified weight and level, describing its implementation in some detail and giving examples of its use.
We apply Zagier's result for the traces of singular moduli to construct Borcherds products in higher level cases.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We establish several formulas relating periods of modular forms on quaternion algebras over number fields to special values of L-functions. Our main inputs are the cohomological techniques for working with periods introduced in [Mol21],…
Let $l\geq 3$ and $F$ be a modular form of weight $l/2-1$ on $\mathrm{O}(l,2)$ which vanishes only on rational quadratic divisors. We prove that $F$ has only simple zeros and that $F$ is anti-invariant under every reflection fixing a…
Generalized product formulas and index transforms, involving products of Whittaker's functions of different indices are established and investigated. The corresponding inversion formulas are found. Particular cases cover index transforms…
Quasi-pullback of Borcherds products is an operation of renormalized restriction. It produces a meromorphic modular form on a lower dimensional symmetric domain which is again a Borcherds product. We give an explicit formula for the weakly…