A simple evaluation of a theta value,the Kronecker limit formula and a formula of Ramanujan

The Ramanujan Journal - We evaluate the classic sum $$\sum _{n\in {\mathbb {Z}}} e^{-\pi n^2}$$ . The novelty of our approach is that it does not require any prior knowledge about modular forms,...     

Lattice points in bodies of revolution II

In [3] it was shown that when a three-dimensional smooth convex body has rotational symmetry around a coordinate axis one can find better bounds for the lattice point discrepancy than what is known for more general convex bodies. To accomplish this, however, it was necessary to assume a non-vanishing condition on the third derivative of the generatrix. In this article we drop this condition, showing that the aforementioned bound holds for a wider family of revolution bodies, which includes those with analytic boundary. A novelty in our approach is that, besides the usual analytic methods, it requires studying some Diophantine properties of the Taylor coefficients of the phase on the Fourier transform side.     

Isolation of Pu-isotopes from environmental samples using ion chromatography for accelerator mass spectrometry and alpha spectrometry

A radiochemical method for the isolation of plutonium-isotopes from environmental samples, based on the use of specific extraction chromatography resins for actinides (TEVA^®, Eichrom Industries, Inc.), has been set up in our laboratory and optimised for their posterior determination by alpha spectrometry (AS) or accelerator mass spectrometry (AMS). The proposed radiochemical method has replaced in our lab a well-established one based on the use of a relatively un-specific anion-exchange resin (AG^® 1X8, Bio-rad Laboratories, Inc.), because it is clearly less time consuming, reduces the amounts and molarities of acid wastes produced, and reproducibly gives high radiochemical yields.In order to check the reliability of the proposed radiochemical method for the determination of plutonium-isotopes in different environmental matrixes, twin aliquots of a set of samples were prepared with TEVA^® and with AG^® 1X8 resins and measured by AS. Some samples prepared with TEVA^® resins were measured as well by AMS. As it is shown in the text, there is a comfortable agreement between AS and AMS, which adequately validates the method.     

Some Fourier series with gaps

We examine diverse local and global aspects of the family of Fourier series ∑n ^?α e(n ^k x). In particular, combining number theoretical and harmonic analytic arguments, we study differentiability, Hölder continuity, spectrum of singularities and fractal dimension of the graph.     

Lattice points in rational ellipsoids

We combine exponential sums, character sums and Fourier coefficients of automorphic forms to improve the best known upper bound for the lattice error term associated to rational ellipsoids.     

The fifth chemical revolution: 1973–1999

A new chronology is introduced to address the history of chemistry, with educational purposes, particularly for the end of the twentieth century and here identified as the fifth chemical revolution. Each revolution are considered in terms of the Kuhnian notion of ‘exemplar,’ rather than ‘paradigm.’ This approach enables the incorporation of instruments, as well as concepts and the rise of new subdisciplines into the revolutionary process and provides a more adequate representation of such periods of development and consolidation. The fifth revolution developed from 1973 to 1999 and is characterized by a deep transformation in the very heart of chemistry. That is to say, the size and type of objects (substances), the way in which they must be done and the time in which they are transformed. In one way or another, chemistry’ limits had been set out.     

Primes represented by quadratic polynomials via exceptional characters

Archiv der Mathematik - We estimate the number of primes represented by a general quadratic polynomial with discriminant $$\Delta $$ , assuming that the corresponding real character is exceptional.     

On twisted character sums

In this paper we give a simple proof of a result by Burgess about short sums involving Dirichlet characters and exponentials. Indeed we establish a slightly stronger and more general bound that applies to sums of the form \({\sum_{n=M+1}^{M+N}f(\alpha n)\chi(n)}\), where χ is a non-principal character to the modulus p and f is a smooth 1-periodic function.     

Non-Euclidean visibility problems

We consider the analog of visibility problems in hyperbolic plane (represented by Poincaré half-plane model ℍ), replacing the standard lattice ℤ × ℤ by the orbitz = i under the full modular group SL₂(ℤ). We prove a visibility criterion and study orchard problem and the cardinality of visible points in large circles.