Related papers: Pair correlation statistics for Sato-Tate sequence…
Let E_lambda be a Hilbert space, whose elements are functions spanned by the eigenfunctions of the Laplace-Beltrami operator associated with an eigenvalue lambda>0. The norm of elements in this space is given by the Petersson inner product.…
Quantum Monte Carlo method is used to re-examine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a `correlated pairing', $\langle \tilde{c}_{i\uparrow}…
We consider cuspidal representations in spaces of automorphic forms for the congruence subgroup $\Gamma_0(I)$ of Hilbert modular groups for some number field $F$. To each such representation are associated the eigenvalue $\lambda_j$ of the…
In this paper, we study the Drinfeld cusp forms for $\Gamma_1(T)$ and $\Gamma(T)$ using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators associated to degree one prime ideals acting on the…
The gauge coupling constants in the electroweak standard model can be written as mass ratios, e.g. the coupling constant for isospin interactions $g_2^2=2{m_W^2\over m^2}\sim 2({80\over169})^2\sim{1\over 2.3}$ with the mass of the charged…
We prove that Hecke eigenvalues for any Hilbert and Siegel modular forms are algebraic integers. Our method does not rely on cohomologicality nor Galois representations. We apply the integrality of Hecke eigenvalues for Hilbert modular…
Equal time spin--spin and pair field correlation functions are calculated for a two-chain Hubbard model using a density-matrix numerical renormalization group approach. At half-filling, the antiferromagnetic and pair field correlations both…
Serre and Stark found a basis for the space of modular forms of weight 1/2 in terms of theta series. In this paper, we generalize their result - under certain mild restrictions on the level and character - to the case of weight 1/2 Hilbert…
In the literature, the standard approach to finding bases of spaces of modular forms is via modular symbols and the homology of modular curves. By using the Eichler-Shimura isomorphism, a work by Wang shows how one can use a cohomological…
In this paper, we study the average behaviour of the coefficients of triple product L-functions and some related L-functions corresponding to normalized primitive holomorphic cusp form $f(z)$ of weight $k$ for the full modular group $SL(2,\…
We propose a formulation of the Equivariant Tamagawa Number Conjecture for modular motives with coefficients in universal deformation rings and Hecke algebras; something which seems to have been heretofore missing because the complexes of…
Numerical studies of the Hubbard model and its strong-coupling form, the t-J model, show evidence for antiferromagnetic, d_{x^2-y^2}-pairing and stripe correlations which remind one of phenomena seen in the layered cuprate materials. Here,…
We investigate some key analytic properties of Fourier coefficients and Hecke eigenvalues attached to scalar-valued Siegel cusp forms $F$ of degree 2, weight $k$ and level $N$. First, assuming that $F$ is a Hecke eigenform that is not of…
The standard approach to evaluate Hecke eigenvalues of a Siegel modular eigenform F is to determine a large number of Fourier coefficients of F and then compute the Hecke action on those coefficients. We present a new method based on the…
We extend methods of Greenberg and the author to compute in the cohomology of a Shimura curve defined over a totally real field with arbitrary class number. Via the Jacquet-Langlands correspondence, we thereby compute systems of Hecke…
Using $U_q[SU(2)]$ tensor calculus we compute the two-point scalar operators (TPSO), their averages on the ground-state give the two-point correlation functions. The TPSOs are identified as elements of the Temperley-Lieb algebra and a…
The frequency structure of the superconducting correlations in cuprates gives insights on the pairing mechanism. Here we present an exhaustive study of this problem in the two-dimensional Hubbard model with cellular dynamical mean-field…
We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss…
We study the statistics of pairs from the sequence $(n^\alpha)_{n\in\mathbb{N}^*}$, for every parameter $\alpha \in \, ]0,1[$. We prove the convergence of the empirical pair correlation measures towards a measure with an explicit density.…
In this paper, we investigate the Rankin-Selberg problem over short intervals in families of holomorphic modular forms and Hecke-Maass cusp forms. Our investigation assumes a Lindel\"of-on-average bound for holomorphic modular forms, and…