Oscillatory integrals with phases arising from algebraic number fields
Abstract
We develop a theory of oscillatory integrals whose phase is given by the trace of a polynomial over an algebraic number field. We present an application to the singular integral for a version of Tarry's problem for algebraic integers.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.02776
- arXiv:
- arXiv:2408.02776
- Bibcode:
- 2024arXiv240802776F
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Classical Analysis and ODEs;
- 42B99
- E-Print:
- 40 Pages