Topics in analytic number theory
James Maynard (著者), D. R. Heath-Brown (学位管理者), University of Oxford (学位授与機関)
In this thesis, the author proves results using the circle method, sieve theory and the distribution of primes, character sums, modular forms and Maass forms, and the Granville-Soundararajan theory of pretentiousness. In particular, he proves theorems about partitions and q-series, almost-prime values of polynomials, Gauss sums, modular forms, quadratic forms, and multiplicative functions exhibiting extreme cancellation. This includes a proof of the Alder-Andrews conjecture, generalizations of theorems of Iwaniec and Ono and Soundararajan, and answers to questions of Zagier and Serre, as well as questions of the author in the Granville-Soundararajan theory of pretentiousness
学位論文、学術論文, English, 2013
University of Oxford, [Great Britain], 2013