Generic T-adic exponential sums in one variable

Abstract

The $T$-adic exponential sum associated to a Laurent polynomial in one variable is studied. An explicit arithmetic polygon is proved to be the generic Newton polygon of the $C$-function of the T-adic exponential sum. It gives the generic Newton polygon of $L$-functions of $p$-power order exponential sums.

including update proofs of results of 0802.0271

References in corpus (3)

• Generic exponential sums associated to Laurent polynomials in one variable
• Hodge-Stickelberger polygons for L-functions of exponential sums of P(x^s)
• T-adic exponential sums over finite fields

Cited by in corpus (2)

• T-adic exponential sums over finite fields
• $T$-adic exponential sums of polynomials in one variable