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^*

^*Korresponderande författare för detta arbete

FNT Gemensamma

Forskningsoutput: Arbetsdokument › Vetenskaplig

Sammanfattning

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.

Originalspråk	Engelska
Utgivare	arXiv
Antal sidor	33
Status	Publicerad - 4 mar 2020
MoE-publikationstyp	O2 Other

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title = "Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis",

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.",

keywords = "Prime numbers, Arithmetic progressions, Explicit",

author = "Neea Paloj{\"a}rvi and Anne-Maria Ernvall-Hyt{\"o}nen",

year = "2020",

month = mar,

day = "4",

language = "English",

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AU - Palojärvi, Neea

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

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