Discrete Fourier Transform and L-functions

2025/03/13 by Liu, D.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.09943

Abstract

We give the converse to Dirichlet's theorem on primes in arithmetic progressions by generalizing an old result of Guinand.

Related

• The prime number theorem for primes in arithmetic progressions at large values
• There are infinitely many prime numbers in all arithmetic progressions with first term and difference coprime
• Prime number decomposition of the Fourier transform of a function of the greatest common divisor
• An alternative proof of the Dirichlet prime number theorem
• Refinements for primes in short arithmetic progressions