The fundamental lemma of a relative trace formula for
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 -invariance of the Potts Hamiltonian.
The Generalized Divisor Problem Over Arithmetic Progressions.
The geometry of the third moment of exponential sums
We give a geometric interpretation (and we deduce an explicit formula) for two types of exponential sums, one of which is the third moment of Kloosterman sums over of type . We establish a connection between the sums considered and the number of -rational points on explicit smooth projective surfaces, one of which is a surface, whereas the other is a smooth cubic surface. As a consequence, we obtain, applying Grothendieck-Lefschetz theory, a generalized formula for the third moment of Kloosterman...
The greatest prime factor of the integers in an interval
The greatest prime factor of the integers in an interval
The growth rate of the Dedekind Zeta-function on the critical line
The hybrid mean value of Dedekind sums and two-term exponential sums
In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and asymptotic formula for it.
The hybrid power mean of quartic Gauss sums and Kloosterman sums
The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of one kind fourth hybrid power mean of the quartic Gauss sums and Kloosterman sums, and give an exact computational formula for it.
The Jacobi Sums of Orders Thirteen and Sixty and Related Quadratic Decompositions.
The least primitive root in number fields
The least square-free number in an arithmetic progression.
The Linnik conjecture. A local approach.
The major arcs approximation of an exponential sum over primes
The mean fourth power of real character sums
The moments of infinite series.
The Pólya-Vinogradov inequality for totally real algebraic number fields
The representation of almost all numbers as sums of unlike powers
We prove in this article that almost all large integers have a representation as the sum of a cube, a biquadrate, ..., and a tenth power.
The Schrödinger density and the Talbot effect
We study the local properties of the time-dependent probability density function for the free quantum particle in a box, i.e. the squared magnitude of the solution of the Cauchy initial value problem for the Schrödinger equation with zero potential, and the periodic initial data. √δ-families of initial functions are considered whose squared magnitudes approximate the periodic Dirac δ-function. The focus is on the set of rectilinear domains where the density has a special character, in particular,...