A density result for elliptic Dedekind sums
A density theorem and extreme values of automorphic L-functions at one
We establish a density theorem for symmetric power L-functions attached to primitive Maass forms and explore some applications to extreme values of these L-functions at 1.
A Dimension Formular for a Certain Space of Automorphic Forms of SU (p,1).
A Dirichlet Series Associated to Eisenstein Series of Degree Two.
A Dirichlet series for Hermitian modular forms of degree 2
A Dirichlet series for modular forms of degree n
A factorization of the Selberg zeta function attached to a rank 1 space form.
A few remarks on automorphic functions.
A Fourier summation formula for the symmetric space
A function on the upper half space which is analogous to the imaginary part of log ... (z).
A generalization of Gauss sums and its applications to Siegel modular forms and L-functions associated with the vector space of quadratic forms.
A generalization of level-raising congruences for algebraic modular forms
In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field . We do this for automorphic representations of an arbitrary reductive group over , which is compact at infinity. In the special case where is an inner form of over , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.
A generalization of Rademacher's reciprocity law
We generalize Rademacher's reciprocity formula for the Dedekind sum to a family of cotangent sums. One of the sums in this family is strictly related to the Vasyunin sum, a function defined on the rationals that is relevant to the Nyman-Beurling-Báez-Duarte approach to the Riemann hypothesis.
A generalization of the reciprocity law of multiple Dedekind sums
Various multiple Dedekind sums were introduced by B.C.Berndt, L.Carlitz, S.Egami, D.Zagier and A.Bayad.In this paper, noticing the Jacobi form in Bayad [4], the cotangent function in Zagier [23], Egami’s result on cotangent functions [14] and their reciprocity laws, we study a special case of the Jacobi forms in Bayad [4] and deduce a generalization of Egami’s result on cotangent functions and a generalization of Zagier’s result. Further, we consider their reciprocity laws.
A geometrical approach to the theory of Jacobi forms
A hybrid mean value involving two-term exponential sums and polynomial character sums
Let be a positive integer. For any integers and , the two-term exponential sum is defined by , where . In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.
A hybrid mean value of the Dedekind sums
The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.
A hybrid mean value related to Dedekind sums
The main purpose of this paper is to study a hybrid mean value problem related to the Dedekind sums by using estimates of character sums and analytic methods.
A Hyperbolic Kac-Moody Algebra and the Theory of Siegel Modular Forms of Genus 2.
A larger GL 2 large sieve in the level aspect
In this paper we study the orthogonality of Fourier coefficients of holomorphic cusp forms in the sense of large sieve inequality. We investigate the family of GL 2 cusp forms modular with respect to the congruence subgroups Γ1(q), with additional averaging over the levels q ∼ Q. We obtain the orthogonality in the range N ≪ Q 2−δ for any δ > 0, where N is the length of linear forms in the large sieve.