Venkatesh was awarded the prize for his work in analytic number theory
, homogeneous dynamics, topology, and representation theory.
Apostol, Introduction to analytic number theory
, Springer-Verlag, New York, 1976.
Pan, Basic Analytic Number Theory
, Harbin Institute of Technology Press, Harbin, China, 2016.
They discuss computability in mathematics and the mathematics of universality, the theory of types, analytic number theory
, cryptology, and enigmatic statistics; the computation of processes, including Turing's neural models; mathematical morphogenetic research; the relationship of computability to the physical world and its quantum-mechanical nature; and infinitary computation and the physics of the mind.
In the Annals article, published in 2013, Zhang proved an element of analytic number theory
that had eluded mathematicians for centuries.
Eleven contributions are selected from the eight working groups in the areas of elliptic surfaces and the Mahler measure, analytic number theory
, number theory in functions fields and algebraic geometry over finite fields, arithmetic algebraic geometry, K-theory and algebraic number theory, arithmetic geometry, modular forms, and arithmetic intersection theory.
His primary focuses are in harmonic analysis, PDE, geometric combinatorics, arithmetic combinatorics, analytic number theory
, compressed sensing, and algebraic combinatorics.
Kolesnik, On the estimation of multiple exponential sums, in Recent Progress in Analytic Number Theory
, Symposium Durham, Academic, London, 1981, 1(1979), 231-248.
They expect readers to have a knowledge of analytic number theory
or a book on it handy.
They assume readers to be families with mathematical analysis and analytic number theory
, particularly with an analytical proof of the prime number theorem.