Paper Citation Record · LEDGER

Twelfth moment of Dirichlet L-functions to prime power moduli

As of 16 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 1 inbound Pith citation observation for arXiv:1908.04833.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.04833 v2

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:46:10.887091Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-24T16:06:26.905668Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-24T16:09:39.848332Z

Reference resolution

17 of 17 outbound references displayed

verified exact3
verified fuzzy3
unresolved9
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 356b16e3-6ca5-4386-9931-b67d799b7d40 · outbound

This paper cites p-adic analytic twists and strong subconvexity.

Twelfth moment of Dirichlet L-functions to prime power moduli p-adic analytic twists and strong subconvexity

Reference 1

Resolution: verified exact; doi, observed 2026-08-14T13:46:11.095485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 75bcdf19-504c-4e4d-9e2f-d546588df7d7 · outbound

This paper cites Decoupling, exponential sums and the Riemann zeta function.

Twelfth moment of Dirichlet L-functions to prime power moduli Decoupling, exponential sums and the Riemann zeta function

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-14T13:46:10.795532Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a1a8804-d93c-4aaa-ad18-e7da3cbc71ee · outbound

This paper cites The cubic moment of central values of automorphic L- functions.

Twelfth moment of Dirichlet L-functions to prime power moduli The cubic moment of central values of automorphic L- functions

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-14T13:46:10.801600Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 011e28d4-4ca1-461e-aac4-8a52136cc713 · outbound

This paper cites an unresolved cited work.

Twelfth moment of Dirichlet L-functions to prime power moduli Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-14T13:46:10.809128Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a2e8a69-6056-414c-8231-dff7225cabdc · outbound

This paper cites Hybrid bounds for Dirichlet L-functions.

Twelfth moment of Dirichlet L-functions to prime power moduli Hybrid bounds for Dirichlet L-functions

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-14T13:46:10.815441Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c678d155-cf6a-481b-b618-5ad30467e5d3 · outbound

This paper cites The fourth power mean of Dirichlet’s L-functions.

Twelfth moment of Dirichlet L-functions to prime power moduli The fourth power mean of Dirichlet’s L-functions

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-14T13:46:10.821805Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 551d5b33-7934-42d7-aac4-4dcd73d66687 · outbound

This paper cites The twelfth power moment of the Riemann-function.

Twelfth moment of Dirichlet L-functions to prime power moduli The twelfth power moment of the Riemann-function

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-14T13:46:10.827974Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b64ba46-ebfc-4d6d-a544-b45ae5b42690 · outbound

This paper cites Mean-Value Theorems in the Theory of the Riemann Zeta-Function.

Twelfth moment of Dirichlet L-functions to prime power moduli Mean-Value Theorems in the Theory of the Riemann Zeta-Function

Reference 8

Resolution: malformed identifier; raw_fallback, observed 2026-08-14T13:46:11.253924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a1a19843-a5eb-4649-8c04-59108da21d47 · outbound

This paper cites Estimates for character sums and Dirichlet L-functions to smooth moduli.

Twelfth moment of Dirichlet L-functions to prime power moduli Estimates for character sums and Dirichlet L-functions to smooth moduli

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:46:11.236673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 750a38a5-3f0a-4ac8-a7e3-a53737b71b8b · outbound

This paper cites Analytic number theory.

Twelfth moment of Dirichlet L-functions to prime power moduli Analytic number theory

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-14T13:46:10.845712Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d16c151e-2ab4-450c-8072-9a09c4b4e62e · outbound

This paper cites Sub-Weyl subconvexity for DirichletL-functions to prime power moduli.

Twelfth moment of Dirichlet L-functions to prime power moduli Sub-Weyl subconvexity for DirichletL-functions to prime power moduli

Reference 11

Resolution: verified exact; doi, observed 2026-08-14T13:46:10.954406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 553e6402-a285-467f-89ed-cc15c5c585cc · outbound

This paper cites Spectral theory of the Riemann zeta-function.

Twelfth moment of Dirichlet L-functions to prime power moduli Spectral theory of the Riemann zeta-function

Reference 12

Resolution: malformed identifier; raw_fallback, observed 2026-08-14T13:46:11.218223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 55e0595b-4c19-4b12-a4ce-07a12b762519 · outbound

This paper cites The Twelfth Moment of Dirichlet L-functions with Smooth Moduli.

Twelfth moment of Dirichlet L-functions to prime power moduli The Twelfth Moment of Dirichlet L-functions with Smooth Moduli

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-14T13:46:10.862211Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9db5ce3f-f683-4fc2-9e63-7606f44f4286 · outbound

This paper cites The Weyl bound for Dirichlet $L$-functions of cube-free conductor.

Twelfth moment of Dirichlet L-functions to prime power moduli The Weyl bound for Dirichlet $L$-functions of cube-free conductor

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-14T13:46:10.867809Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42d47edd-b70e-40fd-ac97-b71db37b50e9 · outbound

This paper cites On the sum of characters with respect to a modulus equal to a power of a prime number.

Twelfth moment of Dirichlet L-functions to prime power moduli On the sum of characters with respect to a modulus equal to a power of a prime number

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:46:11.197950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fe4d899c-2298-4b4c-b106-655fe99176eb · outbound

This paper cites The fourth moment of Dirichlet L-functions.

Twelfth moment of Dirichlet L-functions to prime power moduli The fourth moment of Dirichlet L-functions

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:46:11.178474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a9c80db6-d7f3-4831-b25a-74b4a2a1e69f · outbound

This paper cites Arithmetic exponent pairs for algebraic trace functions and applications.

Twelfth moment of Dirichlet L-functions to prime power moduli Arithmetic exponent pairs for algebraic trace functions and applications

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:46:11.132020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

Observation 96ce1315-a043-4249-b072-77dcbfaea339 · inbound

The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound cites this paper.

The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound Twelfth moment of Dirichlet L-functions to prime power moduli

Reference 40

Resolution: verified exact; arxiv_id, observed 2026-05-24T16:09:39.851012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.