Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn Some Exponential Sums Related to the Coulters Polynomial
61
0
0.0
(
0
)
Added by
Minglong Qi
Publication date
2017
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this paper, the formulas of some exponential sums over finite field, related to the Coulters polynomial, are settled based on the Coulters theorems on Weil sums, which may have potential application in the construction of linear codes with few weights.
rate research
Read More
In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which these inequalities hold.
In the present article, we use Robbas method to give an estimation of the Newton polygon for the L function on torus.
Motivated by fractional quantum Hall effects, we introduce a universal space of statistics interpolating Bose-Einstein statistics and Fermi-Dirac statistics. We connect the interpolating statistics to umbral calculus and use it as a bridge to study the interpolation statistics by the principle maximum entropy by deformed entropy functions. On the one hand this connection makes it possible to relate fractional quantum Hall effects to many different mathematical objects, including formal group laws, complex bordism theory, complex genera, operads, counting trees, spectral curves in Eynard-Orantin topological recursions, etc. On the other hand, this also suggests to reexamine umbral calculus from the point of view of quantum mechanics and statistical mechanics.
We deduce Katzs theorems for $(A,B)$-exponential sums over finite fields using $ell$-adic cohomology and a theorem of Denef-Loeser, removing the hypothesis that $A+B$ is relatively prime to the characteristic $p$. In some degenerate cases, the Betti number estimate is improved using toric decomposition and Adolphson-Sperbers bound for the degree of $L$-functions. Applying the facial decomposition theorem in cite{W1}, we prove that the universal family of $(A,B)$-polynomials is generically ordinary for its $L$-function when $p$ is in certain arithmetic progression.
We describe an algorithm that computes possible corners of hypothetical counterexamples to the Jacobian Conjecture up to a given bound. Using this algorithm we compute the possible families corresponding to $gcd(deg(P),deg(Q))le 35$, and all the pairs $(deg(P),deg(Q))$ with $max(deg(P),deg(Q))le 150$ for any hypothetical counterexample.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
