International Mathematics Research Notices

doi: 10.1093/imrn/rnr088pmid: N/A

doi: 10.1093/imrn/rnr087pmid: N/A

doi: 10.1093/imrn/rnr086pmid: N/A

Bilu, Yuri; Parent, Pierre

doi: 10.1093/imrn/rnq141pmid: N/A

We bound the j-invariant of S-integral points on arbitrary modular curves over arbitrary number fields, in terms of the congruence group defining the curve, assuming a certain Runge condition is satisfied by our objects. We then apply our bounds to prove that for sufficiently large prime p, the points of with r < 1 are either cusps or complex multiplication points. This can be interpreted as the non-existence of quadratic elliptic -curves with higher prime-power degree.

Arias-de-Reyna, Sara; Vila, Nria

doi: 10.1093/imrn/rnq144pmid: N/A

In this paper, we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic ℓ > 3 as the Galois group of a tamely ramified Galois extension of . The strategy is to consider the Galois representation ℓ attached to the Tate module at ℓ of a suitable abelian surface. We need to choose the abelian surfaces carefully in order to ensure that the image of ℓ is large and simultaneously maintain a control on the ramification of the corresponding Galois extension. We obtain an explicit family of curves of genus 2 such that the Galois representation attached to the ℓ-torsion points of their Jacobian varieties provides tame Galois realizations of the desired symplectic groups.

Neretin, Yuri A.

doi: 10.1093/imrn/rnq140pmid: N/A

Consider the space of double cosets of the product of n copies of with respect to the diagonal subgroup. We get a parametrization of this space, the radial part of the Haar measure, and explicit formulas for the actions of the group of outer automorphisms of the free group Fn1 and of the braid group of n 1 strings.

Mller, Werner

doi: 10.1093/imrn/rnq146pmid: N/A

Let be a compact locally symmetric space. In this paper, we establish a version of the Selberg trace formula for non-unitary representations of the lattice . On the spectral side appears the spectrum of the flat Laplacian #, acting in the space of sections of the associated flat bundle. In general, this is a non-self-adjoint operator.

Davis, Michael W.; Januszkiewicz, Tadeusz; Leary, Ian J.; Okun, Boris

doi: 10.1093/imrn/rnq151pmid: N/A

We compute the cohomology with group ring coefficients of the complement of a finite collection of affine hyperplanes in . It is nonzero in exactly one degree, namely, the degree equal to the rank of the arrangement.

Deift, Percy; Krasovsky, Igor; Vasilevska, Julia

doi: 10.1093/imrn/rnq150pmid: N/A

We obtain large gap asymptotics for a Fredholm determinant with a confluent hypergeometric kernel. We also obtain asymptotics for determinants with two types of Bessel kernels which appeared in random matrix theory.

Li, Chi

doi: 10.1093/imrn/rnq152pmid: N/A

Based on Donaldson's method, we prove that, for an integral Khler class, when there is a Khler metric of constant scalar curvature, then it minimizes the K-energy. We do not assume that the automorphism group is discrete.