$ZETA zeta

Latest papers

1. Half-sized gaps between zeros of the Riemann zeta function math.NT · 19 Oct · 3 hits

   …hypothesis, we prove that the lower limit of the normalised gaps between consecutive zeros of the Riemann zeta function is at most $1/2$. Our methods utilise a more efficient method for detecting gaps with short…

2. The factorial separation conjecture math.NT · 19 Oct · 1 hit

   …by five is proved under the Generalized Riemann Hypothesis (GRH) for a specified family of Dedekind zeta functions. Here GRH asserts that their nontrivial zeros have real part $1/2$. The arguments combine…

3. Mixed Tate Chabauty--Kim beyond the polylog quotient math.NT · 18 Oct · 1 hit

   …evaluation map in the presence of a nontrivial motivic Galois action, using relations among motivic multiple zeta values. This yields explicit Kim functions involving multiple polylogarithms, as well as an algorithm…

4. Graded Structures of $v$-adic Carlitz Multiple Polylogarithms and $v$-adic Multiple Zeta Values math.NT · 18 Oct · 2 hits

   In this paper, we study $v$-adic Carlitz multiple polylogarithms and $v$-adic multiple zeta values. We prove that, for every finite place $v$ of $\mathbb{F}_q(\theta)$, the natural weight gives a…

5. Double shuffle and naive duality for multiple Dirichlet series math.NT · 17 Oct · 3 hits

   Multiple zeta values admit both iterated-sum and iterated-integral representations, giving rise to the stuffle,…

6. Human Exposition of Claude's 2/3 Theorem on the zeros of zeta math.NT · 17 Oct · 2 hits

   We expose Claude's proof that $N_0(T)\ge 0.6725 N(T)$ where $N(T)$ is the number of zeros of zeta satisfying $0<\mathop{\mathrm{Re}}\rho\le T$, and $N_0(T)$ the number of those zeros that are simple and…

7. Confluence relations, Hoffman basis over \mathbb{Z}_{(2)}, and the Deligne--Drinfeld conjecture math.NT · 16 Oct · 1 hit

   …combination of Hoffman words and explicit confluence relations. This implies that every multiple zeta value is a linear combination of elements of the Hoffman basis with coefficients having odd…

8. Local topological zeta functions of generic symmetric and catalecticant determinantal varieties math.AG · 16 Oct · 3 hits

   We give explicit formulas for the local topological zeta functions at the origin of generic symmetric determinantal varieties and catalecticant determinantal…