Major arcs for Goldbach's problem
By Harald Andrés Helfgott. 2013
56 citations recorded by the source corpus.
The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer n greater than 5 is the sum of three primes. The present paper proves this conjecture. Both the ternary Goldbach conjecture and the binary, or strong, Goldbach conjecture had their origin in an exchange of letters between Euler and Goldbach in 1742. We will follow an approach based on the circle method, the large sieve and exponential sums, supplemented by rigorous computations, including a verification of zeros of L-functions due to D. Platt. The improved estimates on exponential sums are proven in a twin paper by the author.
Subfields: Algebra and Number Theory, Political Science and International Relations
View Paper: https://www.semanticscholar.org/paper/5023895b48f008bebe00569a32fe7fd53c90a85b
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In Algebra and Number Theory
Citations in the corpus
- The ternary Goldbach conjecture is true (2013, methodology): “ 1.3.2. Minor arc bounds: exponential sums and the large sieve. Let m r be the complement of M r. In particular, m = m r 0 is the complement of M = M r 0 . Exponential sum-estimates, such as those in [Helb], give bounds on max 2mr jS(;x)j that decrease with r. 2This parallels the situation in the tr”