Publications [#320389] of Lillian B. Pierce

Papers Published

1. Heath-Brown, DR; Pierce, LB, Simultaneous integer values of pairs of quadratic forms, Journal fur die Reine und Angewandte Mathematik, vol. 2017 no. 727 (June, 2017), pp. 85-143, WALTER DE GRUYTER GMBH [doi]
   (last updated on 2024/04/17)

   Abstract:
   We prove that a pair of integral quadratic forms in five or more variables will simultaneously represent "almost all" pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement.