Past exam papers - University of Sheffield.
Number Theory This is an exciting area of research where ideas are pursued for their own interest while having a variety of applications. Our research group is one of the leading national centres of excellence in Diophantine approximation and analytic number theory.
Investigations involving the theory and applications of the various tools and techniques of mathematical analysis and analytic number theory are remarkably widespread in many diverse areas of the mathematical, biological, physical, chemical, engineering, and statistical sciences. In this Special Issue, we welcome original as well as review-cum-expository research articles dealing with recent.
I work in a number of mathematical areas, but primarily in harmonic analysis, PDE, geometric combinatorics, arithmetic combinatorics, analytic number theory, compressed sensing, and algebraic combinatorics. I am part of the Analysis Group here at UCLA, and also an editor or associate editor at several mathematical journals.
This research school will focus on three major advances in analytic number theory that have emerged in the last few years: prime number theory, number theory in function fields, and the Hardy and Littlewood Circle Method and Diophantine Geometry. Several recent results in all of these areas represent new trends in analytic number theory and the main aim of the lectures is to give a gentle.
Subjects: Number Theory (math.NT); Combinatorics (math.CO) (14) arXiv:2005.06996 ( pdf, ps, other ) Title: Embeddings of maximal tori in classical groups and Hasse principles.
Analytic Number Theory. MATH636. Dirichlet series, the Riemann zeta function and L-functions, solutions to Diophantine equations, the circle method, exponential sums and character sums. Additional topics may include prime number theorems, sieve methods, connections to harmonic analysis, and automorphic forms. Prerequisites: 333, 531 and 502 or equivalent, or permission of instructor.
Elementary and Analytic Theory of Algebraic Numbers by W. Narkiewicz; Number Theory, Fourier Analysis, and Geometric Discrepancy by G. Travaglini. Additionally, some expository and research papers shall be assigned as reading.