Published in Forum Mathematicum
In this paper we consider the sup-norm problem in the context of analytic Eisenstein series for GL 2 {\mathrm{GL}_{2}} over number fields. We prove a hybrid bound which is sharper than the corresponding bound for Maaß forms. Our results generalize those of Huang and Xu where the case of Eisenstein series of square-free levels over the base field ℚ ...
Published in Forum Mathematicum
The spectrum of the Laplacian operator on the positive theta line bundle over the quasi-torus reduces to eigenvalues π ℓ {\pi\ell} , ℓ = 0 , 1 , … {\ell=0,1,\ldots{}} , which are called Landau levels. This paper discusses the coherent state transform for each eigenspace associated with a Landau level. We construct a unitary transform valid for ea...
Published in Forum Mathematicum
In this paper, we prove a genuine analogue of the Wiener Tauberian theorem for L p , 1 ( G ) {L^{p,1}(G)} ( 1 ≤ p
Published in Forum Mathematicum
In this paper we show that how the representation theory of subcategories (of the category of modules over an Artin algebra) can be connected to the representation theory of all modules over some algebra. The subcategories dealing with are some certain subcategories of the morphism categories (including submodule categories studied recently by Ring...
Published in Forum Mathematicum
Let G n {G_{n}} denote either the group SO ( 2 n + 1 , F ) {\mathrm{SO}(2n+1,F)} or Sp ( 2 n , F ) {\mathrm{Sp}(2n,F)} over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form 〈 Δ 〉 ⋊ σ {\langle\Delta\rangle\rtimes\sigma} , where 〈 Δ 〉 {\langle\Delta\rangle} denotes ...
Published in Forum Mathematicum
In this paper, we study hybrid subconvexity bounds for class group L-functions associated to quadratic extensions K / ℚ {K/\mathbb{Q}} (real or imaginary). Our proof relies on relating the class group L-functions to Eisenstein series evaluated at Heegner points using formulas due to Hecke. The main technical contribution is the uniform sup norm bou...
Published in Forum Mathematicum
We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a more general classification of commutative monoid structures of rank 0, n - 1 n-1 or 𝑛 on a normal affine vari...
Published in Forum Mathematicum
We establish explicit Ichino’s formulae for the central values of the triple product L-functions with emphasis on the calculations for the real place. The key ingredient for our computations is Proposition 8 which generalizes a result in [P. Michel and A. Venkatesh, The subconvexity problem for GL 2 {\rm GL}_{2} , Publ. Math. Inst. Hautes Études Sc...
Published in Forum Mathematicum
We develop a version of Ekedahl’s geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros.
Published in Forum Mathematicum
Let ℛ {\mathcal{R}} be a finite valuation ring of order q r {q^{r}} . In this paper, we prove that for any quadratic polynomial f ( x , y , z ) ∈ ℛ [ x , y , z ] {f(x,y,z)\in\mathcal{R}[x,y,z]} that is of the form a x y + R ( x ) + S ( y ) + T ( z ) {axy+R(x)+S(y)+T(z)} for some one-variable polynomials R , S , T {R,S,T} , we have | f...
