A partition of a non-negative integer n is any non-increasing sequence of positive integers whose sum is n. As usual, let p(n) denote the number of partitions of n. The partition function satisfies the famous “Ramanujan congruences” declaring that for c ∈ {5, 7, 11} we have for all n ≥ 0 that p(cn+δc) ≡ 0 (mod c), where δc is defined by the congruence 24δc ≡ 1 (mod c). In order to understand th...

This proposal falls broadly in the area of number theory and more specifically in arithmetic geometry. It is concerned with a part of the Birch and Swinnerton-Dyer (BSD) conjecture on elliptic curves and abelian varieties. A fundamental problem of number theory is: given a set of polynomial equations with rational coefficients, find all of its rational solutions and investigate their structure....

A large colony of Cerion has recently been reported from Delray Beach, Florida, far north from the ranges of both native and introduced species of Cerion. Specimens correspond morphologically to the type series of Cerion (Paracerion) tridentatum costellata Pilsbry, 1946, which no longer survives at its type locality (Fort Jefferson, Garden Key, Dry Tortugas, Florida.) Historical data indicate t...

Let N be a prime and let A be a quotient of J0(N) over Q associated to a newform such that the special L-value of A (at s = 1) is non-zero. Suppose that the algebraic part of the special L-value of A is divisible by an odd prime q such that q does not divide the numerator of N−1 12 . Then the Birch and Swinnerton-Dyer conjecture predicts that the q-adic valuations of the algebraic part of the s...

The group of rational points on an elliptic curve is one of the more fascinating number theoretic objects studied in recent times. The description of this group in terms of the special value of the L-function, or a derivative of some order, at the center of the critical strip, as enunciated by Birch and Swinnerton-Dyer is surely one of the most beautiful relationships in all of mathematics; als...

Les kystes péri-neuraux sont des kystes des racines nerveuses trouvés le plus souvent au niveau de la colonne sacrée survenant entre des couches de recouvrement de la périnèvre et l'endonèvre. Ils sont relativement rares et la plupart d'entre eux sont asymptomatiques. Certains kystes d'eux peuvent exercer une pression sur les éléments nerveux, entraînant d'une sciatique, d'un déficit moteur et ...

A fundamental problem of number theory is: given a set of polynomial equations with rational coefficients, find all of its rational solutions and investigate their structure. In many cases, the Birch and Swinnerton-Dyer conjecture (henceforth abbreviated BSD conjecture) predicts the existence of such solutions and describes some of their structure without actually finding the solutions. The imp...

The present study shows the results of monitoring the atmospheric pollen in the atmosphere of an area of natural vegetation, the Hornachuelos Natural Park, Cordoba, southern Spain, during a six years (1998-2003). Special attention was paid in the seasonal and intra-diurnal characteristics of airborne allergenic pollen. During this period, 31 pollen types were described, some of them rare in aer...

The overall goal of this study is to develop remote sensing desertification indicators for drylands, in particular using the capabilities of imaging spectroscopy (hyperspectral imagery) to derive soil and vegetation specific properties linked to land degradation status. For this purpose, a hyperspectral (field and remote sensing) monitoring program was established in the Natural Park Cabo de Ga...

Astronomers and biologists have had telescopes and microscopes respectively to aid in their research. With the advent of the computer, mathematicians acquired a powerful tool, using which they could generate data, make conjectures and try turning them into theorems — this was the dawn of the golden age of experimental mathematics. My research sits at the crossroads of number theory, algorithms ...