The determinant of the Laplacian on the n-sphere
The Dirichlet series of : On an error term associated with its coefficients
The distribution of zeros of Epstein zeta functions over GLₙ
The fundamental theorem of prehomogeneous vector spaces modulo (With an appendix by F. Sato)
For a number field with ring of integers , we prove an analogue over finite rings of the form of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where is a big enough prime ideal of and . In the appendix, F.Sato gives an application of the Theorems 1.1, 1.3 and the Theorems A, B, C in J.Denef and A.Gyoja [Character sums associated to prehomogeneous vector spaces, Compos. Math., 113(1998), 237–346] to the functional equation of -functions...
The least prime which does not split completely.
The Maaß Space and Hecke Operators.
The Mean Square of Dirichlet Series Associated with Automorphic Forms.
The product of two Dirichlet series
The second moment of Dirichlet twists of Hecke L-functions
The second moment of quadratic twists of modular L-functions
We study the second moment of the central values of quadratic twists of a modular -function. Unconditionally, we obtain a lower bound which matches the conjectured asymptotic formula, while on GRH we prove the asymptotic formula itself.
The second moment of the symmetric square -functions.
The Spectral Mean Square of Hecke L-functions on the Critical Line
The universality of zeta-functions attached to certain cusp forms
The universality theorem for Hecke L-functions
The universality theorem for L-functions associated with ideal class characters
The value of the Estermann zeta functions at s=0
The zeta function of a hypergraph.
Twisted Dirichlet series and distributions
Twists and resonance of -functions, I
We obtain the basic analytic properties, i.e. meromorphic continuation, polar structure and bounds for the order of growth, of all the nonlinear twists with exponents of the -functions of any degree in the extended Selberg class. In particular, this solves the resonance problem in all such cases.
Two-variable zeta functions and regularized products.