Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis

Neea Palojärvi; Anne-Maria Ernvall-Hytönen

Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis

Neea Palojärvi, Anne-Maria Ernvall-Hytönen^*

^*Corresponding author for this work

FNT Common

Research output: Working paper › Scientific

Abstract

We prove an explicit error term for the ψ(x,χ) function assuming the Generalized Riemann Hypothesis. Using this estimate, we prove a conditional explicit bound for the number of primes in arithmetic progressions.

Original language	English
Publisher	arXiv
Number of pages	33
Publication status	Published - 4 Mar 2020
MoE publication type	O2 Other

Keywords

Prime numbers
Arithmetic progressions
Explicit

Cite this

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abstract = "We prove an explicit error term for the ψ(x,χ) function assuming the Generalized Riemann Hypothesis. Using this estimate, we prove a conditional explicit bound for the number of primes in arithmetic progressions.",

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AU - Ernvall-Hytönen, Anne-Maria

PY - 2020/3/4

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N2 - We prove an explicit error term for the ψ(x,χ) function assuming the Generalized Riemann Hypothesis. Using this estimate, we prove a conditional explicit bound for the number of primes in arithmetic progressions.

AB - We prove an explicit error term for the ψ(x,χ) function assuming the Generalized Riemann Hypothesis. Using this estimate, we prove a conditional explicit bound for the number of primes in arithmetic progressions.

KW - Prime numbers

KW - Arithmetic progressions

KW - Explicit

UR - https://arxiv.org/abs/2003.01925

M3 - Working paper

BT - Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis

PB - arXiv

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Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis

Abstract

Keywords

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