Assing, Edgar
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 ...

Ziyat, Mohammed
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...

Rana, Tapendu
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

Hafezi, Rasool
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...

Matić, Ivan
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 ...

Nordentoft, Asbjørn Christian
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...

Dzhunusov, Sergey Zaitseva, Yulia
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...

Cheng, Yao
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...

Browning, Tim D. Heath-Brown, Roger
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.

Ham, Le Quang Van The, Nguyen Tran, Phuc D. Vinh, Le Anh
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...