TL;DR
This paper extends the Rogers integral formula to the adeles of number fields and proves second moment formulas, broadening its applicability to classical and recent problems in number theory.
Contribution
It introduces an adelic version of the Rogers integral formula and establishes second moment formulas for key cases, expanding its use in number theory.
Findings
Extended Rogers integral formula to adeles of number fields
Proved second moment formulas for important cases
Enabled applications to classical and recent number theory problems
Abstract
We formulate and prove the extension of the Rogers integral formula to the adeles of number fields. We also prove the second moment formulas for a few important cases, enabling a number of classical and recent applications of the formula to extend immediately to any number field.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Mathematical Identities · Analytic Number Theory Research