
TL;DR
This paper constructs a generating polynomial that encodes the generic Newton polygon for a family of exponential sums, providing a tool to understand their properties across large primes.
Contribution
It introduces a generating polynomial over the rationals for the generic Newton polygon of exponential sums of the family f = x^d + a x^s, revealing key properties.
Findings
The generating polynomial encodes the generic Newton polygon for large primes.
It determines the Newton polygon at each prime p when p is sufficiently large.
The polynomial reveals key properties of the exponential sums' L functions.
Abstract
In this paper we construct a generating polynomial over the rationals for the generic Newton polygon for the L function of exponential sums of the family of f = x^d+ a x^s parameterized by a, and prove some of its key properties. The generating polynomial encodes information of and determines the generic Newton polygon at each prime p when p is large enough, and vice versa.
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