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We examine the moments of the number of lattice points in a fixed ball of volume V for lattices in Euclidean space which are modules over the ring of integers of a number field K. In particular, denoting by ωK the number of roots of unity in K, we ...
We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...
Higher Green functions are real-valued functions of two variables on the upper half-plane, which are bi-invariant under the action of a congruence subgroup, have a logarithmic singularity along the diagonal, and satisfy the equation f = k(1−k) f ; here i ...
In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness results in several key dimensions (d = 1, 8, 24), in which a function could be uniquely reconstructed from the values of it and its Fourier transform on a discr ...
In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that ...
The precise momentum dependence of the superconducting gap in the iron-arsenide superconductor Ba1−xKxFe2As2 (BKFA) with Tc=32 K was determined from angle-resolved photoemission spectroscopy (ARPES) via fitting the distribution of the quasiparticle density ...
In this thesis we study algebraic cycles on Shimura varieties of orthogonal type. Such varieties are a higher dimensional generalization of modular curves and their important feature is that they have natural families of algebraic cycles in all codimesions ...
The disordered flux line lattice in single crystals of the slightly overdoped BaFe2−xCoxAs2 (x=0.19, Tc=23 K) superconductor is studied by magnetization measurements, small-angle neutron scattering, and magnetic force microscopy (MFM). In the whole range o ...
Building on Viazovska’s recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particul ...
One of the most unique and robust experimental facts about iron-based superconductors is the renormalization of the electronic band dispersion by factor of 3 and more near the Fermi level. Obviously related to the electron pairing, this prominent deviation ...
