اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn Katzs $(A,B)$-exponential sums
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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.
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