Current task: —

E-011 — Li coefficients n<=2000 from arithmetic side (Bombieri-Lagarias Thm 2 eta-form; flint Stieltjes + Arb zeta; zero-free); ALL CHECKS PASS

08-18-2026 · 2000 rows · script research/numerics/scripts/E-011-li-coefficients-arithmetic.py

Metadata

Bombieri-Lagarias Theorem 2 (eta-form): lambda_n from Stieltjes constants (parallel mpmath sweep, series division) + Arb zeta values; zero-free

Validation checks

V1_lambda1_exact PASS
V2_matches_E008_zero_side PASS
V3_all_positive PASS
V5_precision_self_consistent PASS

Key values

lambda_10.0230957089661210338143102479065
lambda_102.27933936319316
lambda_100118.603775376791
lambda_10002326.05316168647
lambda_n_max5351.7595383815
asymptotic_ratio_at_n_max1.0021569
self_consistency_rel_dev6.67e-705

Parameters

n_max2000
dps1000
arb_bits3530

Caveats

Chart

Data preview (2000 rows total)

nlambda_nlambda_over_refined_asymptotic
10.02309570896612103381431025-0.020432700758
20.09234573522804667038572849-0.058912215273
30.207638920554324803791492-0.119122286233
40.3687904794922416385905115-0.210889970949
50.5755427144611774524311064-0.353514714452
60.8275660122823792974250028-0.588300705195
71.12446011757095949058282-1.02072451437
81.465755677147060632655515-2.02206821942
91.850916048382534155326045-6.48384724156
102.27933936319315774369303410.8737531567
112.7503608382201960603545473.64389346629
123.2632553206246198480790862.4253619238
133.8172400578479459871043681.92997353236
144.4114776786805985120806411.66548065172
155.0450793720267934585351111.50356300876
165.7171082488687926394190671.39597654231
176.4265828721172029011455411.32052398569
187.1724809382917229592529711.26556966769
197.9537430943119003048082251.22442756614
208.7692768720932151295994611.19298386123
219.6179607231429189823613961.16856970436
2210.498648134934874697087561.14937901773
2311.410171810515100840911791.13414681838
2412.351347892551317017034061.12196150599
2513.320980212891575799943361.11215025682