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February 19, 2026MathematicsOpen Access

Notes on Number Theory

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Authors

MSMiroslav StoenchevSGSlavi GeorgievVTVenelin Todorov

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Overview

Examines connections between algebra and number theory, highlighting key structures and theorems.

Key Points

  • This paper aims to connect themes of pure algebra with underlying principles in algebraic and analytic number theory.
  • Surveys core topics in number theory and algebraic structures.
  • Explores finite extensions of Q and algebraic number fields.
  • Discusses cyclotomic fields, Galois structures, and ramification in extensions.
  • Introduces elliptic curves and examines related conjectures and L-functions.
  • Highlights connections using Laplace and Mellin transforms.
  • Establishes a framework for understanding algebraic number fields and their properties.
  • Clarifies the role of cyclotomic fields in bonding algebra with number theory.
  • Links fractional calculus to number theory through convolution operators and zeta-functions.
  • Identifies connections between L-functions, Dirichlet series, and algebraic concepts.

Cite This Study

Stoenchev et al. (2026) studied this question.

synapsesocial.com/papers/6996a788ecb39a600b3ed521https://doi.org/10.3390/math14040697
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