On Weierstra{\ss} semigroups at one and two points and their corresponding Poincar\'e series

The aim of this paper is to introduce and investigate the Poincar\'e series associated with the Weierstra{\ss} semigroup of one and two rational points at a (not necessarily irreducible) non-singular projective algebraic curve defined over a finite field, as well as to describe their functional equations in the case of an affine complete intersection.Comment: Beginning of Section 3 and Subsection 3.1 were modifie

On certain remarkable curves of genus five

We characterize the genus five curves having exactly 24 Weierstass points, and in particular we show that they are unramified double covering of the Fermat's quartic

Letters of Sophie Germain preserved in Florence

Published here, and discussed, are some manuscripts and a letter of Sophie Germain concerning her work on Fermat's last theorem. These autographs, held at the Bibliothèque Nationale of Paris, at the Moreniana Library of Florence and at the University Library of Göttingen, contribute to a substantial revaluation of her work on this subject

Abel's surviving manuscripts including the one recently found in London

We list and locate all N.H. Abel's surviving manuscripts and trace a short history of them. We also present, with some comments, a manuscript that was discovered in London very recently. In the note we give a brief account of what happened to the manuscript that Abel sent to A.L. Crelle ad we report the very recent discovery of the memoirs that Crelle published under the title "Remarques sur quelque propriete generales d'une certaine sorte de functions trascendentes"

On the Correspondence of Sophie Germain

The aim of this paper is to give a thorough account of the presently known correspondence of Sophie Germain, as well as the history of its discovery and editing. In particular, we will focus on the correspondence with Gauss and Guglielmo Libri

The rationality of certain moduli spaces associated to half-canonical extremal curves

AbstractWe prove the existence of a coarse, irreducible moduli space Cm−1g (resp. Cm−1g,1) for (resp. pointed) subcanonical extremal curves of level m−1 and genus g in PCr. When g=3r, r≥4, r≠5, odd (resp. even) we show that C23r (resp. C23r,1) is rational

On certain spaces associated to tetragonal curves of genus 7 and 8

Lecture Notes in Pure and Applied Mathematics series, Marcel Dekke