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Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with…
The metric Bezout Theorem proved in an earlier paper can be extended to a derivative version that compares derivatives of the algebraic distance of a point $\theta$ to two properly intersecting cycles in projective space with the…
In this paper, we give some explicit evaluations of multiple zeta-star values which are rational multiple of powers of $\pi^2$.
When performing a conceptual analysis of a concept, philosophers are interested in all forms of expression of a concept in a text---be it direct or indirect, explicit or implicit. In this paper, we experiment with topic-based methods of…
Ihara, Kaneko, and Zagier proved the derivation relation for multiple zeta values. The first named author obtained its counterpart for finite multiple zeta values in $\mathcal{A}$. In this paper, we present its generalization in…
This note describes continued fraction representations for the rational approximations to the zeta function recently found by the author. It is tempting to think that these continued fractions might be analysed using a souped up version of…
We present an algorithmic approach to the verification of identities on multiple theta functions in the form of products of theta functions $[(-1)^{\delta}a_1^{\alpha_1}a_2^{\alpha_2}\cdots a_r^{\alpha_r}q^{s}; q^{t}]_\infty$, where…
We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient…
We establish the meromorphic continuation of certain multiple zeta functions of generalized Hurwitz type. From this meromorphic continuation, we obtain explicit formulas for their (derivative) values at nonpositive integers along a given…
We define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck--Witt group. We show that this enrichment is related to the topology of the…
We note that a rational $3$-tangle diagram is obtained from a combination of four generators. There is an algorithm to distinguish two rational $3$-tangle diagrams up to isotopy. However, there is no perfect classification about rational…
We introduce a zeta function counting imaginary quadratic number fields by their class numbers. It is proved that such a function is rational depending only on the eight roots of unity of degrees $1$ and $2$. As a corollary, one gets a…
We study mirror symmetric pairs of Calabi--Yau manifolds over finite fields. In particular we compute the number of rational points of the manifolds as a function of the complex structure parameters. The data of the number of rational…
We establish an omega theorem for logarithmic derivative of the Riemann zeta function near the 1-line by resonance method. We show that the inequality $\left| \zeta^{\prime}\left(\sigma_A+it\right)/\zeta\left(\sigma_A+it\right) \right|…
We introduce a new technique for evaluation of series with zeta coefficients and also for evaluation of certain integrals involving the logGamma function. This technique is based on Hankel integral representations of the Hurwitz zeta, the…
A recent paper of Furdui and Valean proves some results about sums of products of "tails" of the series for the Riemann zeta function. We show how such results can be proved with weaker hypotheses using multiple zeta values, and also show…
Motivated by the weighted Hurwitz product on sequences in an algebra, we produce a family of monoidal structures on the category of Joyal species. We suggest a family of tensor products for charades. We begin by seeing weighted derivational…
Assuming the Riemann hypothesis we establish explicit bounds for the modulus of the log-derivative of Riemann's zeta-function in the critical strip.
We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta…
Potential theory for rational approximation is reviewed by means of examples computed with the AAA algorithm.