MATH-417: Number theory II.b - selected topics

Lectures in this course (9)

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Explores inverse limits, profinite completions, and Hausdorff topologies in group theory and topology.

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

Covers the duality principle in linear algebra and its implications in mathematics.

Covers integration on H_pxH and arithmetic topics, focusing on the Hensel Lemma and the process of finding R and S such that R.S-P=0.

Covers adelic number theory, focusing on properties of maximal open compact subrings and constructions of adelic spaces.

Explores adelic number theory, emphasizing lattices, modules, linear combinations, and Z-linear properties.

Explores the theory of lattices, their properties, and applications in different mathematical contexts, emphasizing local-global principles.

Explores group actions on lattices, emphasizing GL₂(Q) and GL₂(Ag) compatibility and alternative formulations.

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