Systems of Diagonal Equations Over p-Adic Fields

Knapp, Michael P.

doi:10.1112/s002461070000171x

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Cited by 11 publications

(11 citation statements)

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“…suffices for these primes. One can compare this with the result given in [4] for systems of forms which all have the same degree (although this result is improved in [6]). Theorem 1 is a trivial consequence of the following theorem, which is unfortunately somewhat more complicated to state.…”

Section: Introductionmentioning

confidence: 74%

On systems of diagonal forms II

Knapp

2009

Math. Proc. Camb. Phil. Soc.

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Section: Introductionmentioning

confidence: 74%

On systems of diagonal forms II

Knapp

2009

Math. Proc. Camb. Phil. Soc.

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“…In the special case

K = {double-struckQ}_{p}

, Knapp has shown that it suffices for

s

to satisfy

s > \frac{3}{2} R^{2} d^{2}

p > 2

and

s > 4 R^{2} d^{2}

p = 2

[5, Theorem 2], which is the best result to date for this case. The bounds for systems over a general

K

coming from Theorem A thus differ from the best bounds for systems over

Q_{p}

only by a factor of 2.…”

Section: Introductionmentioning

confidence: 99%

Solvability of systems of diagonal equations over p‐adic local fields

Skinner

2020

Proc. London Math. Soc.

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“…There has been much work in the recent literature concerning systems of diagonal equations and their relation to AC (see [6,7,11,12,13,14,15]). In particular, it is known that AC holds for pairs of diagonal forms of equal degree k, except possibly when k takes the form p τ (p − 1) or 3 · 2 τ (p = 2), and that AC holds also for pairs of diagonal forms of distinct odd degrees.…”

Section: Introductionmentioning

confidence: 99%