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We show that for a monic polynomial $f(x)$ over a number field $K$ containing a global permutation polynomial of degree $>1$ as its composition factor, the Newton Polygon of $fmodmathfrak p$ does not converge for $mathfrak p$ passing through all finite places of $K$. In the rational number field case, our result is the only if part of a conjecture of Wan about limiting Newton polygons.
In this paper, we consider the following $(A, B)$-polynomial $f$ over finite field: $$f(x_0,x_1,cdots,x_n)=x_0^Ah(x_1,cdots,x_n)+g(x_1,cdots,x_n)+P_B(1/x_0),$$ where $h$ is a Deligne polynomial of degree $d$, $g$ is an arbitrary polynomial of degree
A conjecture of Le says that the Deligne polytope $Delta_d$ is generically ordinary if $pequiv 1 (!!bmod D(Delta_d))$, where $D(Delta_d)$ is a combinatorial constant determined by $Delta_d$. In this paper a counterexample is given to show that the conjecture is not true in general.
In this paper, we study the Newton polygons for the $L$-functions of $n$-variable generalized Kloosterman sums. Generally, the Newton polygon has a topological lower bound, called the Hodge polygon. In order to determine the Hodge polygon, we explici
Let $X_0^{star}(k,n,s)$ denote the sum of all multiple zeta-star values of weight $k$, depth $n$ and height $s$. Kaneko and Ohno conjecture that for any positive integers $m,n,s$ with $m,ngeqslant s$, the difference $(-1)^mX_0^{star}(m+n+1,n+1,s)-(-1
It is well known that for any prime $pequiv 3$ (mod $4$), the class numbers of the quadratic fields $mathbb{Q}(sqrt{p})$ and $mathbb{Q}(sqrt{-p})$, $h(p)$ and $h(-p)$ respectively, are odd. It is natural to ask whether there is a formula for $h(p)/h(