I am an incoming undergraduate at Zhengzhou University. I have studied analytic number theory independently for several years, with particular interests in the Riemann zeta function, exponential sums, trace formulas, and spectral transforms. I also develop machine-checked formalizations in Lean 4.
- Analytic number theory
- The Riemann zeta function and
L-functions - Exponential sums and the distribution of primes
- Trace formulas and spectral transforms
- Formalized mathematics in Lean 4
- Asymptotic Analysis and Phase Transition of the Bessel--Kuznetsov Transform with an Oscillatory Phase, Integral Transforms and Special Functions (2026). Author manuscript on arXiv
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A counterexample to Sun's sign conjecture for cotangent permanents, preprint (2026). It proves the exact identity
t'_{29} = 84,643,985,981,440 > 0, giving a counterexample atp = 29to the cotangent sign inequality in Zhi-Wei Sun's Conjecture 4.7(ii). Source repository · Lean 4 formalization · PalomarPALOMAR-2026-08-27-000019v1 -
A Constructive Heuristic Sieve for the Twin Prime Problem, arXiv:2507.03107.
- A two-certificate trace--energy deduction for simple zeros of the
Riemann zeta function.
The draft gives the candidate lower bound
liminf_(T -> infinity) N_0^s(T,2T) / N(T,2T) >= 0.6733169771424713.... Permanent Zenodo record · PalomarPALOMAR-2026-08-29-000004v1
The new finite-dimensional supporting-plane and exact-arithmetic layer is formalized in Lean 4. The upstream interval certificates and analytic interface remain imported inputs; the result is a research-draft candidate pending independent mathematical review.