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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Local Method for Compositional Inverses of Permutation Polynomials
置换 多项式复合逆 局部方法
2023/4/18
In this talk, we will talk about a local method to find compositional inverses of all PPs, some new PPs and their compositional inverses are given.
Littlewood asked how small the ratio $||f||_4/||f||_2$ (where $||.||_\alpha$ denotes the $L^\alpha$ norm on the unit circle) can be for polynomials $f$ having all coefficients in $\{1,-1\}$, as the de...
The variance of the number of prime polynomials in short intervals and in residue classes
variance the number of prime polynomials short intervals residue classes Number Theory
2012/4/23
We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial i...
A Unified Generating Function of the q-Genocchi Polynomials with their Interpolation Functions
Genocchi numbers and polynomials q-Genocchi numbers and polynomials Number Theory
2011/9/23
Abstract: The purpose of this paper is to construct of the unification q-extension Genocchi polynomials. We give some interesting relations of this type of polynomials. Finally, we derive the q-extens...
Representation of powers by polynomials over function fields and a problem of Logic
problem of Logic polynomials over function fields Number Theory
2011/9/15
Abstract: We solve a generalization of B\"uchi's problem in any exponent for function fields, and briefly discuss some consequences on undecidability. This provides the first example where this proble...
Some Congruences of Kloosterman Sums and their Minimal Polynomials
Congruences of Kloosterman Sums Minimal Polynomials
2011/1/18
We prove two results on Kloosterman sums over finite fields, using Stickelberger’s theorem and the Gross-Koblitz formula. The first result concerns the minimal polynomial over Q of a Kloosterman sum, ...
Congruences concerning Legendre polynomials II
Legendre polynomial congruence character sum binary quadratic form
2011/2/22
Let p > 3 be a prime, and let m be an integer with p ∤ m. In the paper we solve some conjectures of Z.W.
Let p > 3 be a prime, and let m be an integer with p ∤ m. In the paper we solve some conjectures of Z.W. Sun concerning Pp−1 k=0 (6k)! mk(3k)!k!3 (mod p), and show that for integers m, n w...
Let p be an odd prime. In the paper, by using the properties of Legendre polynomials we prove some congruences for P p−1 2 k=0 2k k 2 m−k (mod p2). In particular, we confirm se...
Rational approximations to values of Bell polynomials at points involving Euler's constant and zeta values
Bell polynomials Euler's constant zeta values
2010/11/22
In this paper, we present new explicit simultaneous rational approximations converging sub-exponentially to the values of Bell polynomials at the points of the form $(\gamma, 1! (2a+1)\zeta(2), 2!\zet...
On summable form of Poisson-Mehler kernel for big q-Hermite and Al-Salam-Chihara polynomials
Poisson-Mehler kernel big q-Hermite Al-Salam-Chihara polynomials
2010/11/15
Using special technique of expansion of the ratio of densities we obtain simple closed forms for certain kernels analogous to Poisson-Mehler, also asymmetric, for certain values of parameters, proving...