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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.
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 t
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
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 pair