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商洛学院数学与计算机应用学院初等数论课件Chapter 1 Prime Numbers.
Prime tight frames
divisible frames equiangular tight frames frames harmonic tight frames prime frames spectral tetris frames tight frames
2015/12/10
We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of pri...
PRIME SPECIALIZATION IN HIGHER GENUS II
Bateman–Horn conjecture Hardy–Littlewood conjecture
2015/7/6
We continue the development of the theory of higher-genus M¨obius periodicity
that was studied in Part I for odd characteristic, now treating asymptotic questions and
the case of characteristic 2. T...
Prime Decomposition in Iterated Towers and Discriminant Formulae
iterated extension radical extension
2014/12/8
We explore certain arithmetic properties of iterated extensions. Namely, we compute the index associated to certain families of iterated polynomials and determine the decomposition of prime ideals in ...
Strong pseudoprimes to the first 9 prime bases
Strong Pseudoprimes Chinese Remainder Theorem
2012/7/9
Define $\psi_m$ to be the smallest strong pseudoprime to the first $m$ prime bases. The exact value of $\psi_m$ is known for $1\le m \le 8$. Z. Zhang have found a 19-decimal-digit number $Q_{11}=3825\...
A Diophantine problem with prime variables
Diophantine problems with prime variables Number Theory
2012/6/14
We study the distribution of the values of the form $\lambda_1 p_1 + \lambda_2 p_2 + \lambda_3 p_3^k$, where $\lambda_1$, $\lambda_2$ and $\lambda_3$ are non-zero real number not all of the same sign,...
L^2-norms of exponential sums over prime powers
Primes in short intervals Diophantine problems with primes Number Theory
2012/6/14
We study a suitable mean-square average of primes in short intervals, generalizing Saffari-Vaughan's result. We then apply it to a ternary Diophantine problem with prime variables.
A Diophantine problem with a prime and three squares of primes
Goldbach-type theorems Hardy-Littlewood method diophantine inequalities
2012/6/14
We prove that if $\lambda_1$, $\lambda_2$, $\lambda_3$ and $\lambda_4$ are non-zero real numbers, not all of the same sign, $\lambda_1 / \lambda_2$ is irrational, and $\varpi$ is any real number then,...
On the stratification of noncommutative prime spectra
algebraic group rational action algebraic torus rational ideal prime spectrum stratification
2012/6/6
We study rational actions of an algebraic torus G by automorphisms on an associative algebra R. The G-action on R induces a stratification of the prime spectrum of R which was introduced by Goodearl a...
Positive integer n is between two adjacent prime numbers square, the well-established number of product even distribution of the formula (S) andformula (L), According to the prime number theorem, Mert...
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...
Prime component-preservingly amphicheiral link with odd minimal crossing number
component-preservingly amphicheiral link minimal crossing number Tait's conjecture
2012/3/1
For every odd integer $c\ge 21$, we raise an example of a prime component-preservingly amphicheiral link with minimal crossing number $c$.
In this paper we extend the proof of the twin prime conjecture to prove the Sophie Germain prime conjecture and to attack the Cunningham chain. We show also that there are infinitely many composites i...
There always exists at least one prime between x and x+x^{1/2} when x is sufficiently large
Pprime distribution of primes
2011/9/21
In this paper one has shown that there always exists at least one pseudo prime number between x and x+x^{1/2} when x is sufficiently large for a pseudo sequence of odd numbers, so it also is true that...
There always exists at least one prime between x and x+log^2(x) when x> =8
Prime distribution of primes
2011/9/21
In this paper one has shown that there always exists at least one pseudo prime number between x and x+log^2(x), so it also is true that there always exists at least one real prime number for the real ...