Hypergeometric L-functions in average polynomial time

@article{Costa2020HypergeometricLI,
  title={Hypergeometric L-functions in average
polynomial time},
  author={Edgar Costa and Kiran S. Kedlaya and David Roe},
  journal={Open Book Series},
  year={2020}
}
We describe an algorithm for computing, for all primes $p \leq X$, the mod-$p$ reduction of the trace of Frobenius at $p$ of a fixed hypergeometric motive in time quasilinear in $X$. This combines the Beukers--Cohen--Mellit trace formula with average polynomial time techniques of Harvey et al. 
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References

SHOWING 1-10 OF 64 REFERENCES
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Finite hypergeometric functions
Finite hypergeometric functions are complex valued functions on finite fields which are the analogue of the classical analytic hypergeometric functions. From the work of N.M.Katz it follows that
SageMath
  • the Sage Mathematics Software System (Version 9.0),
  • 2020
volume 124 of Annals of Mathematics Studies
  • Princeton University Press, Princeton, NJ,
  • 1990
Frobenius structures on hypergeometric equations
We give an exposition of Dwork's construction of Frobenius structures associated to generalized hypergeometric equations via the interpretation of the latter due to Gelfand-Kapranov-Zelevinsky in the
MATH
TLDR
It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
Une introduction aux motifs (motifs purs, motifs mixtes, périodes)
La theorie des motifs, introduite par A. Grothendieck il y a 40 ans et demeuree longtemps conjecturale, a connu depuis une quinzaine d'annees des developpements spectaculaires. Ce texte a pour
A Course in p-adic Analysis
1 p-adic Numbers.- 2 Finite Extensions of the Field of p-adic Numbers.- 3 Construction of Universal p-adic Fields.- 4 Continuous Functions on Zp.- 5 Differentiation.- 6 Analytic Functions and
Finite hypergeometric functions
The ideas of this thesis are based on an article written by F. Beukers and A. Mellit. They have shown that, when defined over Q, finite hypergeometric sums correspond to point counting on projective
...
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