Goldbach's Problem with Almost Twin Primes

Abstract: The Binary Goldbach and Twin Prime conjectures have shaped the development of Analytic Number Theory in the the last century in fundamental manner. Among the strongest approximative results that we know are a power saving bound on the exceptional set of the first conjecture, proved by Montgomery and Vaughan, and Chen’s result on almost Twin Primes.

In this talk I present joint work with J. Teräväinen that aims to combine the two just mentioned results. More precisely, we show a power saving exceptional set bound for sums of two primes $p_1, p_2$ such that $p_1+2$ has at most 2, $p_2+2$ at most 3 prime divisors. This improves previous results of this type in both strength of saving and number of prime divisors of the shifted primes. Our proof uses a wide range of techniques. I will give a sketch of how they play together and what the limitations are.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

Participants are welcome to stay following the talks to have further discussions with the speakers or meet other audience members.

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