An extension of the Apéry number supercongruence
An identity involving Dedekind sums and generalized Kloosterman sums
The various properties of classical Dedekind sums have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums . The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of...
An inequality for local unitary Theta correspondence
Given a representation of a local unitary group and another local unitary group , either the Theta correspondence provides a representation of or we set . If is fixed and varies in a Witt tower, a natural question is: for which is ? For given dimension there are exactly two isometry classes of unitary spaces that we denote . For let us denote the minimal of the same parity of such that , then we prove that where is the dimension of .
An infinite ferm in the universal deformation space of Galois representations.
I hope this article will be helpful to people who might want a quick overview of how modular representations fit into the theory of deformations of Galois representations. There is also a more specific aim: to sketch a construction of a point-set topological'' configuration (the image of an infinite fern'') which emerges from consideration of modular representations in the universal deformation space of all Galois representations. This is a configuration hinted previously, but now, thanks to some...
An integral involving the generalized zeta function.
An integral representation of standard automorphic functions for unitary groups.
An integral transform and its applications.
An integrality criterion for elliptic modular forms
Let be an elliptic modular form level of N. We present a criterion for the integrality of at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to the iterates of the Maaß differential operators.
An isomorphism between polynomial eigenfunctions of the transfer operator and the Eichler cohomology for modular groups.
An odd square as a sum of an odd number of odd squares
An orthogonal test of the L-functions Ratios Conjecture, II
An ...-Result for the Coefficients of Cusp Forms.
An ...-Theorem for Ramanujan's ...-Function.
Analogs of Δ(z) for triangular Shimura curves
We construct analogs of the classical Δ-function for quotients of the upper half plane 𝓗 by certain arithmetic triangle groups Γ coming from quaternion division algebras B. We also establish a relative integrality result concerning modular functions of the form Δ(αz)/Δ(z) for α in B⁺. We give two explicit examples at the end.
Analyse semi-classique de la formule des traces de Selberg (début)
Analyse spectrale des formes automorphes et séries d'Eisenstein.
Analyse spectrale et prolongement analytique : séries d’Eisenstein, fonctions et nombre de solutions d’équations diophantiennes
Analytic continuation of representations and estimates of automorphic forms.
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
Andrianov' s L-functions associated to Siegel wave forms of degree two.