Related papers: Regularization of p-adic String Amplitudes, and Mu…

In this article, we study the local behaviour of the multiple zeta functions at integer points and write down a Laurent type expansion of the multiple zeta functions around these points. Such an expansion involves a convergent power series…

Geometric zeta functions of Ihara and Hashimoto are generalized to higher rank. The $p$-adic version of the Patterson conjecture is proven.

We study the resurgent structure of Walcher's real topological string on general Calabi-Yau manifolds. We find trans-series solutions to the corresponding holomorphic anomaly equations, at all orders in the string coupling constant, by…

In \citenospec{MR1097615} several spectral sequences for (global and local) Iwasawa modules over (not necessarily commutative) Iwasawa algebras (mainly of $p$-adic Lie groups) over $\Z_p$ are established, which are very useful for…

This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…

We prove partial regularity for minimizers of quasiconvex functionals of the type $\int_\Omega f(x,Du) dx$ with $p(x)$ growth with respect to the second variable. The proof is direct and uses a method of $A$-harmonic approximation.

This is a review on the two first parts of our work on $p$-adic multiple zeta values at $N$-th roots of unity ($p$MZV$\mu_{N}$'s), the $p$-adic periods of the crystalline pro-unipotent fundamental groupoid of $\mathbb{P}^{1} -…

In this paper we study the zeta functions associated to the minimal spherical principal series of representations for a class of reductive p-adic symmetric spaces, which are realized as open orbits of some prehomogeneous spaces. These…

In this paper, we study the quantization errors of modulo sigma-delta modulated finite, asymptotically-infinite, infinite causal stable ARMA processes. We prove that the normalized quantization error can be taken as a uniformly distributed…

We study the topological string on local P2 with O-plane and D-brane at its real locus, using three complementary techniques. In the A-model, we refine localization on the moduli space of maps with respect to the torus action preserved by…

In 2011 Lemahieu and Van Proeyen proved the Monodromy Conjecture for the local topological zeta function of a non-degenerated surface singularity. We start from their work and obtain the same result for Igusa's p-adic and the motivic zeta…

We quantitatively relate the resonance sets of topologically finite infinite-area hyperbolic surfaces with no cusps to the resonance sets of certain metric graphs via the spine graph construction. In particular, we prove the existence of…

We study a class of nonlocal systems which can be described by a local scalar field diffusing in an auxiliary radial dimension. As examples p-adic, open and boundary string field theory are considered on Minkowski,…

A new algorithm to calculate Coulomb wave functions with all of its arguments complex is proposed. For that purpose, standard methods such as continued fractions and power/asymptotic series are combined with direct integrations of the…

A consistent procedure for regularization of divergences and for the subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov-Kleinert…

We investigate a pattern in the $\alpha'$ expansion of tree-level open superstring amplitudes which correlates the appearance of higher depth multiple zeta values with that of simple zeta values in a particular way. We rephrase this…

This article presents an approach to the algebraic functional equation for Selmer complexes, which in turn have applications in the Iwasawa theoretic study of Rankin-Selberg products of the Hida and Coleman families. Our treatment…

We study how the dimensional regularization works in the light-cone gauge string field theory. We show that it is not necessary to add a contact term to the string field theory action as a counter term in this regularization at least at the…

Let $f_{\mathrm{new}}$ be a classical newform of weight $\geq 2$ and prime to $p$ level. We study the arithmetic of $f_{\mathrm{new}}$ and its unique $p$-stabilisation $f$ when $f_{\mathrm{new}}$ is $p$-irregular, that is, when its Hecke…

There has been an avalanche of recent research on multiple zeta values. We propose dividing identities for multiple zeta values into structural and specific types. Structural identities are valid for any generalized multiple zeta function,…