We compute the imaginary part of scalar four-point functions in the AdS/CFT correspondence relevant to N = 4 super Yang-Mills theory. We find that unitarity of the AdS supergravity demands that the imaginary parts of the correlation functions factorize into products of lower-point functions. We include the exchange diagrams for scalars as well as gravitons and find explicit expressions for the ...

The table of Gradshteyn and Ryzhik contains many integrals with integrands of the form R1(x) (lnR2(x)) m, where R1 and R2 are rational functions. In this paper we describe some examples where the logarithm appears to a single power, that is m = 1, and the poles of R1 are either real or purely imaginary.

For each odd prime p, we prove the existence of infinitely many real quadratic fields which are p-rational. Explicit imaginary and bi-quadratic p-rational also given for p. Using a recent method developed by Greenberg, deduce Galois extensions Q with group isomorphic to an open subgroup GLn(Zp), n=4 n=5 at least all primes p<192.699.943.

Let L be a quadratic imaginary field, inert at the rational prime p. Fix an integer n ≥ 3, and let M be the moduli space (in characteristic p) of principally polarized abelian varieties of dimension n equipped with an action by OL of signature (1, n−1). We show that each Newton stratum of M, other than the supersingular stratum, is irreducible.

An even unimodular 72-dimensional lattice Γ having minimum 8 is constructed as a tensor product of the Barnes lattice and the Leech lattice over the ring of integers in the imaginary quadratic number field with discriminant −7. The automorphism group of Γ contains the absolutely irreducible rational matrix group (PSL2(7)× SL2(25)) : 2.

In this paper we prove an analogue of Mordell’s inequality for lattices in finite-dimensional complex or quaternionic Hermitian space that are modules over a maximal order in an imaginary quadratic number field or a totally definite rational quaternion algebra. This inequality implies that 16dimensional Barnes-Wall lattice has optimal density among all 16-dimensional lattices with Hurwitz struc...

A hyperelliptic function eld can be represented as imaginary or as real quadratic extension of the rational function eld. We show that in both cases one can compute in the class group of the function eld using reduced ideals of the orders involved. Furthermore, we show how the two representations are connected and compare the computational complexity.

In this paper we prove a version of Mordell’s inequality for lattices in finite-dimensional complex or quaternionic Hermitian space that are modules over a maximal order in an imaginary quadratic number field or a totally definite rational quaternion algebra. This inequality implies that 16dimensional Barnes-Wall lattice has optimal density among all 16-dimensional lattices with Hurwitz structu...

Let p be a rational prime number. We refine Brauer’s elementary diagonalisation argument to show that any system of r homogeneous polynomials of degree d, with rational coefficients, possesses a non-trivial p-adic solution provided only that the number of variables in this system exceeds (rd) d 1 . This conclusion improves on earlier results of Leep and Schmidt, and of Schmidt. The methods exte...

Rational filter functions improve convergence of contour-based eigensolvers, a popular algorithm family for the solution of the interior eigenvalue problem. We present an optimization method of these rational filters in the Least-Squares sense. Our filters out-perform existing filters on a large and representative problem set, which we show on the example of FEAST. We provide a framework for (n...