${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$ is the archetypal magnetoelectric (ME) material, which has a linear coupling between electric and magnetic polarizations. Quadratic ME effects are forbidden for point group of ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$, due to space-time inversion symmetry. In films grown by sputtering, we find signature quadratic effect that not found in bulk single crystals. We us...

We introduce a practical synchronous stream cipher with provable security named QUAD. The cipher relies on the iteration of a multivariate quadratic system of m equations in n < m unknowns over a finite field. The security of QUAD is provably reducible to the conjectured intractability of the MQ problem, namely solving a multivariate system of quadratic equations.

We prove that the representations numbers of a ternary definite integral quadratic form defined over Fq[t], where Fq is a finite field of odd characteristic, determine its integral equivalence class when q is large enough with respect to its successive minima. Equivalently, such a quadratic form is determined up to integral isometry by its theta series.

We use methods from representation theory and invariant theory to compute differential operators invariant under the action of the Jacobi group over a complex quadratic field. This allows us to introduce Maass-Jacobi forms over complex quadratic fields, which are Jacobi forms that are also eigenfunctions of an invariant differential operator. We present explicit examples via Jacobi-Eisenstein s...

in cite{p}, park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}&amp;&amp; |f(x+y)+f(x-y)-2f(x)-2f(y)| &amp;&amp; qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|andbegin{eqnarray}&amp;&amp; left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}r...

We study a Kloosterman sum for GL4 and prove that it is equal to an exponential sum over a quadratic number field. This identity has applications in a relative trace formula for GL4 which might be used to give a new proof of quadratic base change and characterize its image.