Pith. sign in

REVIEW 1 cited by

Moments of the Riemann zeta-function

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0612106 v2 pith:74ULGM22 submitted 2006-12-04 math.NT

K. Soundararajan This is my paper · ORCID
classification math.NT
keywords momentsriemannboundzeta-functionassumingasymptoticconjecturedcritical
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Assuming the Riemann Hypothesis we obtain an upper bound for the moments of the Riemann zeta-function on the critical line. Our bound is nearly as sharp as the conjectured asymptotic formulae for these moments. The method extends to moments in families of $L$-functions.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Tsang-range high-moment bound for $\operatorname{Im}\log L(\tfrac12+it,\chi)$ under GRH

    math.NT 2026-06 unverdicted novelty 5.0 of 10

    Under GRH, the 2k-th moment of Im log L(1/2+it, χ) for fixed odd squarefree conductor q is bounded by (C_K k log log(qT))^k for k up to order log log(qT).

Pith tools