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Rational quadrilaterals and tetrahedra -- the involutions of Kummer, Heegner and Regge
S. J. Patterson
This paper is devoted to questions concerning rational quadrilaterals and rational tetrahedra. In both cases there is a finite group which acts on the set. In the case of rational…
On a question of H. A. Schwarz
Samuel J. Patterson
This paper is a contribution to the study of tetrahedra with rational side lengths and rational volume. The problem can be formulated as a study of a hyperelliptic variety attached…
Selberg sums - a new perspective
Samuel J. Patterson
Selberg sums are the analogues over finite fields of certain integrals studied by Selberg in in 1940s. The original versions of these sums were introduced by R.J.Evans in 1981 and,…
The Fourier coefficients of metaplectic theta series on GL(2) over rational function fields
Samuel J. Patterson
The idea of the metaplectic theta function was introduced by Tomio Kubota in the 1960s. These theta functions are constructed as residues of Eisenstein series and are only known co…