What question did this study set out to answer?

This research aims to construct a p-adic L-function for symplectic representations of GL(N) over number fields.

On p-adic L-functions for symplectic representations of GL (N) over number fields

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Randomized trial constructs p-adic L-functions in number fields, indicating their interpolation properties in various settings.

This research aims to construct a p-adic L-function for symplectic representations of GL(N) over number fields.
Constructed a p-adic L-function for regular non-critical spin p-refinement of \( \pi \) to Q-parahoric level.
Showed interpolation of critical L-values at p, including cyclotomic variations.
Investigated growth conditions for the constructed p-adic L-function.
Interpolate all standard critical L-values of \( \pi \) at p.
Satisfactory growth condition for \( L_p(\tilde{\pi}) \) established, particularly when \( \tilde{\pi} \) is ordinary.

Chris Williams (2026) studied this question.

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View Full Paper

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Authors

Randomized trial constructs p-adic L-functions in number fields, indicating their interpolation properties in various settings.

This research aims to construct a p-adic L-function for symplectic representations of GL(N) over number fields.
Constructed a p-adic L-function for regular non-critical spin p-refinement of \( \pi \) to Q-parahoric level.
Showed interpolation of critical L-values at p, including cyclotomic variations.
Investigated growth conditions for the constructed p-adic L-function.
Interpolate all standard critical L-values of \( \pi \) at p.
Satisfactory growth condition for \( L_p(\tilde{\pi}) \) established, particularly when \( \tilde{\pi} \) is ordinary.

Chris Williams (2026) studied this question.

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