Related papers: Rational Products of Singular Moduli

We obtain bounds on the number of triples that determine a given pair of dot products arising in a vector space over a finite field or a module over the set of integers modulo a power of a prime. More precisely, given $E\subset \mathbb…

We study the class of modules, called cosilting modules, which are defined as the categorical duals of silting module. Several characterizations of these modules and connections with silting modules are presented. We prove that Bazzoni…

We establish a one-to-one correspondence between conjugacy classes of any Hecke group and irreducible systems of poles of rational period functions for automorphic integrals on the same group. We use this correspondence to construct…

Recently, Bruinier and Ono found an algebraic formula for the partition function in terms of traces of singular moduli of a certain non-holomorphic modular function. In this paper we prove that the rational polynomial having these singuar…

We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of…

New families of algebras and DG algebras with two simple modules are introduced and described. Using the twisted tensor product operation, we prove that such algebras have finite global dimension, and the resulting DG algebras are smooth.…

In this note, inspired by the proof of the Kirillov-Reshetikhin conjecture, we consider tensor products of Kirillov-Reshetikhin modules of a fixed node and various level. We fix a positive integer and attach to each of its partitions such a…

In this paper, we find all Fibonacci numbers which are products of two Pell numbers and all Pell numbers which are products of two Fibonacci numbers.

We prove that the generating function of the positive singular braid monoid is rational and we give the exact formula for such monoid on three strands.

We prove that the moduli space of tetragonal curves of genus g>6 is rational when g is congruent to 1, 2, 5, 6, 9, 10 modulo 12 and not equal to 9, 45.

In the present work, we investigate certain algebraic and differential properties of the orthogonal polynomials with respect to a discrete-continuous Sobolev-type inner product defined in terms of the Jacobi measure.

Let $\mhu$ be the moduli space of semi-stable pure sheaves of class $u$ on a smooth complex projective surface $X$. We specify $u=(0,L,\chi(u)=0),$ i.e. sheaves in $u$ are of dimension $1$. There is a natural morphism $\pi$ from the moduli…

We prove that the class of log canonical rational singularities is closed under the basic operations of the minimal model program. We also give some supplementary results on the minimal model program for log canonical surfaces.

We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.

Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…

For a fixed pair and fixed exponents, we prove the discreteness of log discrepancies over all log canonical triples formed by attaching a product of ideals with given exponents.

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

This is my talk on the Bourbaki seminar, November 1996. It contains an elementary introduction to Borcherds' product formulas.

We prove a result that enables us to calculate the rational homotopy of a wide class of spaces by the theory of minimal models.

We classify $G$-solid rational surfaces over the field of complex numbers.