A path integral approach to lattice point problems
نویسنده
چکیده
The main problem in (planar) lattice point theory consists in counting lattice points under the graph of positive functions supported on [0,M] and with radius of curvature comparable to M . We prove that, in some sense motivated by Feynman path integral formulation of Quantum Mechanics, for “most” functions the lattice error term in the area approximation is O(M1/2+ε). This complements Jarník construction of curves with an optimal O(M2/3) error term. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.
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