東工大 数論・幾何学セミナー：Gautami Bhowmik 氏

The classical Goldbach problem examines the possibility of expressing even integers as the sum of two primes. The associated generating function gives satisfactory asymptotics under the Riemann Hypothesis and obtaining sufficiently good error terms unconditionally is equivalent to solving the famous hypothesis. In joint work with K. Halupczok, K. Matsumoto and Y. Suzuki, we consider the case where the summands are in arithmetic progression and obtain asymptotics assuming now a conjecture on distinct zeros of Dirichlet $L$-functions. The existence of good error terms gives information on the the location of zeros of these functions.