ANTONIO ALARC´ON ABSTRACT. In this paper we construct complete minimal surfaces with boundary in R 3 of arbitrary finite topology. For any arbitrary finite topological type we find a compact Riemann surface M, an open domain M ⊂ M with the fixed topological type, and a conformal complete minimal immersion X : M → R 3 which can be extended to a continuous map X : M → R 3 , such that X |∂M is an ...

We study the possibility of extending ghost systems with higher spin to a logarithmic conformal field theory. In particular we are interested in c = −26 which turns out to behave very differently to the already known c = −2 case. The energy momentum tensor cannot be built anymore by a combination of derivatives of generalized symplectic fermion fields. Moreover, the logarithmically extended the...

A quasi Riemann surface is defined to be a certain kind of complete metric space Q whose integral currents are analogous to the integral currents of a Riemann surface. In particular, they have properties sufficient to express Cauchy-Riemann equations on Q. The prototypes are the spaces D 0 (Σ)m of integral 0-currents of total mass m in a Riemann surface Σ (usually called the integral 0-cycles o...

In this paper we treat the classical Riemann zeta function as a of three variables: one is usual complex 1 -dimensional, customly denoted s , another two are infinite dimensional, denote them b = { n } ∞ and z . When gets function. Our goal in to study meromorphic continuation ζ ( ) triple

We present a new method for proving non-holonomicity of sequences, which is based on results about the number of zeros of elementary and of analytic functions. Our approach is applicable to sequences that are defined as the values of an elementary function at positive integral arguments. We generalize several recent results; e.g., non-holonomicity of the logarithmic sequence is extended to rati...

ABSTRACT. Under two assumptions, we determine the distribution of the difference between two functions each counting the numbers 6 x that are in a given arithmetic progression modulo q and the product of two primes. The two assumptions are (i) the Extended Riemann Hypothesis for Dirichlet L-functions modulo q, and (ii) that the imaginary parts of the nontrivial zeros of these L-functions are li...

The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler’s results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function as a finite sum of double zeta values involving binomial coefficients. Here, we establish a q-analog of Euler’s decomposition formula. More specifically, we s...

In this paper we conjecture that the generating function of the intersection numbers on the moduli spaces of Riemann surfaces with boundary, constructed recently by R. Pandharipande, J. Solomon and R. Tessler and extended by A. Buryak, is a taufunction of the KP integrable hierarchy. Moreover, it is given by a simple modification of the Kontsevich matrix integral so that the generating function...

We describe an algorithm which rapidly computes the coefficients of elements of small norm in quadratic fields modulo a positive integer. Our method requires that an approximation of the natural logarithm of that quadratic field element is known to sufficient accuracy. To demonstrate the efficiency and utility of our method, we apply it to eliminate a number of exceptional cases of a theorem of...