Related papers: On a conjecture of Furusho over function fields
We prove that all but finitely many zeros of Weng's zeta function for a Chevalley group defined over $\Q$ are simple and on the critical line under some reasonable geometric hypothesis.
We propose a field-theoretic interpretation of Ruelle zeta function, and show how it can be seen as the partition function for $BF$ theory when an unusual gauge fixing condition on contact manifolds is imposed. This suggests an alternative…
In this paper we define a symmetric zeta function. We show that it can be analytically continued to a meromorphic function on $\mathbb{C}^3$ with only simple poles at some special hyperplanes. We also calculate the value of a multiple…
We establish finite analogues of the identities known as the Aoki-Ohno relation and the Le-Murakami relation in the theory of multiple zeta values. We use an explicit form of a generating series given by Aoki and Ohno.
Pazuki and Pengo defined a Northcott property for special values of zeta functions of number fields and certain motivic $L$-functions. We determine the values for which the Northcott property holds over function fields with constant field…
We prove Fujita's log spectrum conjecture. It follows from the ACC of a suitable set of pseudo-effective thresholds.
We give a reformuation of the Tate conjecture for a surface over a finite field in terms of suitable affine open subsets. We then present three attempts to prove this reformulation, each of them falling short. Interestingly, the last two…
We give non-torsion counterexamples against the integral Tate conjecture for finite fields. We extend the result due to Pirutka and Yagita for prime numbers 2,3,5 to all prime numbers.
Minor technical changes. Section 4 improved.
A theorem of Tate and Turner says that global function fields have the same zeta function if and only if the Jacobians of the corresponding curves are isogenous. In this note, we investigate what happens if we replace the usual…
We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension…
We prove a "discrete analogue" for Taelman's class modules of certain Conjectures formulated by R. Greenberg for cyclotomic fields.
In the present paper, we provide a new analogy between number fields and 1-dimensional function fields over finite fields from the viewpoint that the maximal cyclotomic extension of a number field is analogous to the constant field…
We give new closed and explicit formulas for "multiple zeta values" at non-positive integers of generalized Euler-Zagier multiple zeta-functions. We first prove these formulas for a small convenient class of these multiple zeta-functions…
We prove the Iwasawa main conjecture over the arithmetic $\mathbb{Z}_p$-extension for semistable abelian varieties over function fields of characteristic $p>0$.
This work is an example driven overview article of recent works on the connection of multiple zeta values, modular forms and q-analogues of multiple zeta values given by multiple Eisenstein series.
Let $L$ be a solvable Lie algebra of dimension less than or equal to 4 over finite fields. We compute and record, in explicit symbolic form, the zeta functions enumerating subalgebras or ideals of $L$, and study their properties. We also…
Inspired by the theory of Hodge correlators due to Goncharov and by the plectic principle of Nekov\'a\v{r} and Scholl, we construct higher plectic Green functions and give a higher order generalization of Hecke's formula for abelian…
In this note, we study the special values for zeta functions of totally real fields using the Shintani's cone decomposition. We prove certain congruence between the special values for zeta functions under the prime degree field extension.…
We give an a geometric interpretation of the Hasse-Arf theorem for function fields using the recently proved Oort conjecture.