Data for The p-Adic Valuations of Weil Sums of Binomials

The paper can be found at:

D. J. Katz, P. Langevin, S. Lee, and Y. Sapozhnikov) The p-Adic Valuations of Weil Sums of Binomials, Journal of Number Theory, 181: 1-26 (2017).

A preprint version is available at:

arXiv: 1608.04047 [math.NT]

The work of Katz, Lee, and Sapozhnikov on this paper and the accompanying materials here was supported in part by the National Science Foundation under Grant DMS 1500856.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

If you are interested in using any code or data presented here for your research, please contact me at email: [my first name] [dot] [my last name] [at] csun [dot] edu

The data file that documents a verification of Conjecture 6.1 in the paper for all fields with less than 10¹³ elements and the data file that documents a verification of Conjecture 6.2 in the paper for all moduli tⁿ-1 with tⁿ less than 3*10⁹ (along with summary files that describe how to read the data files) are presented here. An overall description of the contents is in readme.txt.

Conjecture 6.1 verification
for all fields
with less than
10¹³ elements sharp-ten-to-thirteen.txt
sharp-ten-to-thirteen-summary.txt

Conjecture 6.2 verification
for all moduli
tⁿ-1 with tⁿ
less than 3*10⁹ three-times-ten-to-nine.txt
three-times-ten-to-nine-summary.txt

The program used to produce the data files are described in readme.txt. The executable code, compiled for the AMD64 architecture under GNU/Linux, is presented here.

Conjectures 6.1 and 6.2 verifications ayb

Conjecture 6.1	verification for all fields with less than 10¹³ elements	sharp-ten-to-thirteen.txt sharp-ten-to-thirteen-summary.txt
Conjecture 6.2	verification for all moduli tⁿ-1 with tⁿ less than 3*10⁹	three-times-ten-to-nine.txt three-times-ten-to-nine-summary.txt