Description

CACAAG seminar.

Speaker: Priyamvad Srivastav.

Affiliation: IMSc, Chennai.

Date and Time: Thursday 18 April, 5.15 pm - 6.15 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Product of primes in arithmetic progression.

Abstract: Let $q$ be a positive integer and let $(a,q)=1$ be a given

residue class. Let $p(a,q)$ denote the least prime congruent to $a

\mod{q}$. Linnik's theorem tells us that there is a constant $L>0$, such

that the $p(a,q) \ll q^L$. The best known value today is $L = 5.18$.

A conjecture of Erdos asks if there exist primes $p_1$ and $p_2$, both

less than $q$, such that $p_1 p_2 \equiv a \mod{q}$. Recently, Ramar\'{e}

and Walker proved that for all $q \geq 2$, there are primes $p_1, p_2,

p_3$, each less than $q^{16/3}$, such that $p_1 p_2 p_3 \equiv a \mod{q}$.

Their proof combines additive combinatorics with sieve theoretic

techniques. We sketch the ideas involved in their proof and talk about a

joint work with Olivier Ramar\'{e}, where we refine this method and obtain

an improved exponent of $q$.

Speaker: Priyamvad Srivastav.

Affiliation: IMSc, Chennai.

Date and Time: Thursday 18 April, 5.15 pm - 6.15 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Product of primes in arithmetic progression.

Abstract: Let $q$ be a positive integer and let $(a,q)=1$ be a given

residue class. Let $p(a,q)$ denote the least prime congruent to $a

\mod{q}$. Linnik's theorem tells us that there is a constant $L>0$, such

that the $p(a,q) \ll q^L$. The best known value today is $L = 5.18$.

A conjecture of Erdos asks if there exist primes $p_1$ and $p_2$, both

less than $q$, such that $p_1 p_2 \equiv a \mod{q}$. Recently, Ramar\'{e}

and Walker proved that for all $q \geq 2$, there are primes $p_1, p_2,

p_3$, each less than $q^{16/3}$, such that $p_1 p_2 p_3 \equiv a \mod{q}$.

Their proof combines additive combinatorics with sieve theoretic

techniques. We sketch the ideas involved in their proof and talk about a

joint work with Olivier Ramar\'{e}, where we refine this method and obtain

an improved exponent of $q$.

Description

Ramanujan Hall, Department of Mathematics

Date

Thu, April 18, 2019

Start Time

5:15pm-6:15pm IST

Duration

1 hour

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Wed, April 17, 2019 7:41pm IST