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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Density of orbits and arithmetic degrees of automorphisms of projective threefolds
射影三重 轨道密度 自同构 算术度
2023/4/18
The Zariski dense orbit conjecture of the arithmetic dynamic is to study the existence of a rational point P with a Zariski dense orbit of a dominant rational self-map f of a projective variety X. Whe...
An integer $n$ is said to be \textit{arithmetic} if the arithmetic mean of its divisors is an integer. In this paper, using properties of the factorization of values of cyclotomic polynomials, we char...
On Character Sums and Exponential Sums over Generalized Arithmetic Progressions
Character Sums Exponential Sums Generalized Arithmetic Progressions Number Theory
2012/6/19
We study upper bounds for sums of Dirichlet characters. We prove a uniform upper bound of the character sum over all proper generalized arithmetic progressions, which generalizes the classical Polya a...
Geodesic restrictions of eigenfunctions on arithmetic surfaces
Geodesic restrictions of eigenfunctions arithmetic surfaces Number Theory
2012/4/23
Let X be an arithmetic hyperbolic surface, {\psi} a Hecke-Maass form, and {\gamma} a geodesic segment on X. We obtain a power saving over the local bound of Burq-G\'erard-Tzvetkov for the L^2 norm of ...
Every prime larger than 3 is arithmetic mean of other two primes
prime distribution of primes arithmetic progression Goldbach conjecture
2011/9/21
In this paper a new stronger proposition has been advanced and shown, that is, every prime larger than 3 is arithmetic mean of other two primes, and other important propositions that there are infinit...
Dismal Arithmetic
Dismal Arithmetic Number Theory
2011/8/26
Abstract: Dismal arithmetic is just like the arithmetic you learned in school, only simpler: there are no carries, when you add digits you just take the largest, and when you multiply digits you take ...
On Extending the Langlands-Shahidi Method to Arithmetic Quotients of Loop Groups
automorphic L-functions Eisenstein series loop groups
2010/12/10
We discuss certain Eisenstein series on arithmetic quotients of loop groups, ˆG , which are associated to cusp forms on finite-dimensional groups associated with maximal parabolics of ˆG .