Checks · The unfolded zeros of the Riemann zeta function do not form a Riesz basis of exponentials

Recorded output over the first 100,000 zeros

The keys, in order: n, the number of zeros; sup_abs_d, the largest displacement, 1.12869, with argmax its index (94,352) and gamma_argmax its height; first_cross_index, the first displacement of size at least 1/4 (the 9th zero), with gamma_first_cross its height; centered_sup, the largest displacement after the best centering, cstar; mean_d and rms_d; count_abs_ge_quarter, the 43,588 displacements of size at least 1/4; D_M, the largest block mean for each block length from 1 to 4,096, falling from 1.129 to 0.00049; and min_gap, the smallest unfolded gap, 0.02186, with its index and height. These match Section 7 and Table 1 to the printed digits. The file records no date.

Output of

Verification program for the Kadec and Avdonin statistics over 100,000 zeros (checks/verify_kadec_1e5.py), shown beside it on that page

Written by

verify_kadec_1e5.py, a program by Claude Fable 5.1 (Anthropic)

Size

866 bytes

SHA-256

b7bb26d20e645df26c3ba86e0acb97a8238f0ede844d73b7de7375bf5f442f65

The paper's pageEvery file published with itThis file on GitHub