L-function

C11531

concept

An L-function is a complex analytic function, typically expressed as a Dirichlet series with an Euler product, that encodes deep arithmetic information about objects such as numbers, fields, or algebraic varieties.

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All labels observed (6)

Label	Occurrences
L-function canonical	4
zeta function	2
Euler product	1
L-function theory object	1
exceptional zero of Dirichlet L-function	1
generalization of Riemann zeta function	1

Description generation (CDg)

The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.

Instruction

generate a one-sentence description for a given conceptual class.
# Response Format
Return only the sentence: "Description: [one-sentence description of the conceptional class]"

Input

Class: L-function

Generated description

An L-function is a complex analytic function, typically expressed as a Dirichlet series with an Euler product, that encodes deep arithmetic information about objects such as numbers, fields, or algebraic varieties.

Instances (9)

Instance	Via concept surface
Hasse–Weil zeta function	zeta function
Dirichlet L-functions	—
Dedekind zeta functions surface form: Dedekind zeta function	—
Euler products for automorphic L-functions	Euler product
Riemann zeta function	—
Siegel zero	exceptional zero of Dirichlet L-function
Selberg zeta function	zeta function
Artin L-functions	—
Hurwitz zeta function	generalization of Riemann zeta function