相关论文: A number field extension of a question of Milnor

The Chowla--Milnor conjecture predicts the linear independence of certain Hurwitz zeta values. In this paper, we prove that for any fixed integer $k \geqslant 2$, the dimension of the $\mathbb{Q}$-linear span of…

In this paper, we prove a version of the universality theorem for the Hurwitz zeta-function in the case where the parameter is algebraic and irrational. Then we apply the result to show that many of such Hurwitz zeta-functions have…

We produce generalizations of Iwasawa's `Riemann-Hurwitz' formula for number fields. These generalizations apply to cyclic extensions of number fields of degree p^n for any positive integer n. We first deduce some congruences and…

Let Z(X) be the number of degree-d extensions of F_q(t) with bounded discriminant and some specified Galois group. The problem of computing Z(X) can be related to a problem of counting F_q-rational points on certain Hurwitz spaces.…

In this article, our aim is to extend the research conducted by Kurokawa and Wakayama in 2003, particularly focusing on the $q$-analogue of the Hurwitz zeta function. Our specific emphasis lies in exploring the coefficients in the Laurent…

Spencer Bloch and the author formulated a general conjecture (Tamagawa number conjecture) on the relation between values of zeta functions of motives and arithmetic groups associated to motives. We discuss this conjecture, and describe some…

The purpose of this paper is two-fold. First, we consider the classical Mordell--Tornheim zeta values and their alternating version. It is well-known that these values can be expressed as rational linear combinations of multiple zeta values…

We answer a question of Drungilas-Dubickas in the affirmative under the assumption of standard conjectures on smooth numbers in polynomial sequences. This gives evidence against the "Dubickas Conjecture", which Ka\v{c}inskait\.e and…

In this article, we aim to extend the research conducted by Chatterjee and Garg in 2024, particularly focusing on the $q$-analogue of the generalized Stieltjes constants. These constants constitute the coefficients in the Laurent series…

The Milnor conjecture has been a driving force in the theory of quadratic forms over fields, guiding the development of the theory of cohomological invariants, ushering in the theory of motivic cohomology, and touching on questions ranging…

In this paper we derive two expressions for the Hurwitz zeta function involving the complete Bell polynomials in the restricted case where q is a positive integer greater than 1. The arguments of the complete Bell polynomials comprise the…

We prove the second author's "denominator conjecture" [40] concerning the common denominators of coefficients of certain linear forms in zeta values. These forms were recently constructed to obtain lower bounds for the dimension of the…

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…

The Riemann zeta identity at even integers of Lettington, along with his other Bernoulli and zeta relations, are generalized. Other corresponding recurrences and determinant relations are illustrated. Another consequence is the application…

In this article, we have studied transformation formulas of zeta function at odd integers over an arbitrary number field which in turn generalizes Ramanujan's identity for the Riemann zeta function. The above transformation leads to a new…

The central binomial series is a subject that has been extensively studied, for example in the context of the irrationality of Riemann zeta values. In this paper, the Hurwitz version of the central binomial series is defined by adding one…

The multiple zeta values (MZV) are a set of real numbers with a beautiful structure as an algebra over the rational numbers. They are related to maybe the most important conjecture on mathematics today, the Riemann hypothesis. In this paper…

This paper provides a systematic study of symmetry properties for cyclotomic multiple Hurwitz zeta values with multiple variables and parameters by applying the methods of contour integration and the residue theorem. The main contributions…

We prove nonlinear relation on multiple Hurwitz-Riemann zeta functions. Using analytic continuation of these multiple Hurwitz-Riemann zeta function, we quote at negative integers Euler's nonlinear relation for generalized Bernoulli…

In this paper, we study multiple zeta values (abbreviated as MZV's) over function fields in positive characteristic. Our main result is to prove Thakur's basis conjecture, which plays the analogue of Hoffman's basis conjecture for real…