An online session of the Algebra and Logic Seminar will be held on **January 21, 2022** (Friday) **at 1:00 pm (UTC+2). **A talk on

**On the distribution of αp modulo one for primes p=aq^2+1 with prime q**

**On the distribution of αp modulo one for primes p=aq^2+1 with prime q**

will be delivered by **Tatyana Todorova (FMI, Sofia University, Bulgaria).**

**Abstract. **It is a long-standing conjecture that there are infinitely many primes of the form n^2+1. Several approximations to this problem have been made. Baier and Zhao showed that for any ε > 0, there are infinitely many primes of the form p = aq^2 + 1, where a ≤ p^(5/9+ε). The best known result, due to Matomäki is that there are infinitely many primes of the form p = aq^2 + 1, where a ≤ p^(1/2+ε) and q is a prime.

We prove that there are infinitely many primes of the form p = aq^2 + 1 with a ≤ p^(5/9+ε) and q is a prime, such that ||αp+β||<p^(-θ), where α is irrational, β is real and θ < 1/18.

The seminar will be held via Zoom and everyone can join at:

https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09

Topic: Онлайн семинар на секция “Алгебра и логика”

Time: Jan 21, 2022 01:00 PM Sofia

Meeting ID: 851 3737 5021

Passcode: 035647

Algebra and Logic Department, IMI-BAS

http://www.math.bas.bg/algebra/seminarAiL/

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