The Least Quadratic Nonresidue and Vinogradov's Hypothesis
Keywords:
Iwaniec, deduce, Vinogradov, combiningAbstract
These are rough notes covering the second block of lectures in the “Elementary Methods in Analytic Number Theory” course. In these lectures we will develop several forms of the large sieve inequality, which assert that no sequence can be well correlated with many exponentials or poorly distributed in many arithmetic progressions. By combining the large sieve with Vaughan’s Identity and the Siegel– Walfisz theorem, we will deduce the Bombieri–Vinogradov theorem on the average distribution of primes in progressions. (No originality is claimed for any of the contents of these notes. In particular, they borrow from the books of Davenport [1] and Iwaniec and Kowalski
References
. Davenport. Multiplicative Number Theory. Third edition, revised by Hugh L. Montgomery, published by Springer Graduate Texts in Mathematics. 2000
J. Friedlander and H. Iwaniec. Opera de Cribro. AMS Colloquium Publications, vol. 57. 2010
H. Iwaniec and E. Kowalski. Analytic Number Theory. AMS Colloquium Publications, vol. 53. 2004
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