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HYBRID SUP-NORM BOUNDS FOR HECKE-MAASS CUSP FORMS
Cutting-edge characteristic value hyperbolic measure
2015/8/25
Let f be a Hecke–Maass cusp form of eigenvalue λ and square-free level N. Normalize the hyperbolic measure such that vol(Y0(N)) = 1 and the form f such that kfk2 = 1. It is shown that kfk1 ≪1...
On higher congruences between cusp forms and Eisenstein series
higher congruences cusp forms Eisenstein series Number Theory
2012/6/30
In this paper we present several finite families of congruences between cusp forms and Eisenstein series of higher weights at powers of prime ideals. We formulate a conjecture which describes properti...
Bounds for coefficients of cusp forms and extremal lattices
coefficients of cusp forms extremal lattices
2011/3/1
A cusp form f(z) of weight k for SL2(Z) is determined uniquely by its first ℓ := dim Sk Fourier coefficients. We derive an explicit bound on the nth coefficient of f in terms of its first ℓ...
Equidistribution of cusp forms in the level aspect
Equidistribution cusp forms level aspect
2010/11/11
Let f traverse a sequence of classical holomorphic newforms of fixed weight and increasing squarefree level q tending to infinity. We prove that the pushforward of the mass of f to the modular curve o...
A Spanning Set for the Space of Super Cusp Forms
Automorphic and cusp forms super symmetry semisimple Lie groups partially hyperbolic flows unbounded realization of a complex bounded symmetric domain
2010/1/25
The aim of this article is the construction of a spanning set for the space of super cusp forms on a complex bounded symmetric super domain of rank with respect to a lattice . The main ingredient...