Related papers: Singular moduli refined
We prove a general factorization theorem for Lipschitz summing operators in the context of metric spaces which recovers several linear and nonlinear factorization theorems that have been proved recently in different environments. New…
By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.
We give an explicit formula to express the cohomological pullback functors of Hodge modules under closed immersions of smooth varieties using Verdier specializations and $V$-filtrations of Kashiwara and Malgrange. This was locally obtained…
In this paper, we generalize Dorman's work to estimate singular moduli for higher rank Drinfeld modules. In particular, we give a lower bound on the valuation of singular moduli for Drinfeld modules with complex multiplication by an…
We provide explicit series expansions for the exponential and logarithm functions attached to a rank r Drinfeld module that generalize well known formulas for the Carlitz exponential and logarithm. Using these results we obtain a procedure…
In this paper we examine an inverse problem in the modular theory of von Neumann algebras in the case of finite factors. First we give a characterization of cyclic and separating vectors for finite factors in terms of operators associated…
The Modular Group provides simple proofs of Fermat's representations: X^2+Y^2 for primes congruent to 1 (mod 4) and by X^2+3Y^2 for primes congruent to 1 (mod 3)
The conjecture that every modular lattice is integral is disproved.
Recently Zagier proved a remarkable q-series identity. We show that this identity can also be proved by modifying Franklin's classical proof of Euler's pentagonal number theorem.
In this article we prove a version of Kolyvagin's conjecture for modular forms at non-ordinary primes. In particular, we generalize the work of Wang on a converse to a higher weight Gross-Zagier-Kolyvagin theorem in order to prove the…
We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's…
We prove that affine Coxeter groups are profinitely rigid.
We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a one-dimensional modulation symmetry.
We prove that every profinite group in a certain class with a rational probabilistic zeta function has only finitely many maximal subgroups.
In this paper we present a new efficient algorithm for factoring the RSA and the Rabin moduli in the particular case when the difference between their two prime factors is bounded. As an extension, we also give some theoretical results on…
We show that the multiple divisor functions of integers in invertible residue classes modulo a prime number, as well as the Fourier coefficients of GL(N) Maass cusp forms for all N larger than 2, satisfy a central limit theorem in a…
We extend a new uniqueness result recently proved by Q. Chen, C. Miao and Z. Zhang.
In an important paper, Zagier proved that certain half-integral weight modular forms are generating functions for traces of polynomials in the $j$-function. It turns out that Zagier's work makes it possible to algorithmically compute…
We show that the class of profinite duality groups is closed under group extensions provided that the kernel satisfies some finiteness condition. This extends earlier results of Pletch and of Wingberg.
We propose an explicit and practical algorithm for computing Galois conjugates and irreducible polynomials for special values of modular functions evaluated at CM points associated with imaginary quadratic orders. Our approach builds upon…