Some Problems in Number Theory I: The Circle Problem
Sylvain E. Cappell, Julius L. Shaneson
TL;DR
This paper investigates the problem of counting lattice points within a circle, addressing fundamental issues in number theory related to geometric and analytical methods.
Contribution
It introduces new approaches to estimate the number of lattice points in a circle, improving upon previous bounds and understanding.
Findings
Derived sharper bounds for lattice point counts
Identified key difficulties in the circle problem
Proposed new analytical techniques
Abstract
This paper concerns the number of lattice points in a circle.
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Taxonomy
TopicsMathematics and Applications · Analytic Number Theory Research · History and Theory of Mathematics