identity in analytic number theory
C10782
concept
Identity in analytic number theory is a rigorously proven equality, often involving series, integrals, or arithmetic functions, that reveals structural relationships between number-theoretic objects and underpins analytic techniques such as transforms, convolutions, and explicit formulas.
All labels observed (4)
| Label | Occurrences |
|---|---|
| q-series identity | 2 |
| generalization of the Selberg trace formula | 1 |
| identity in analytic number theory canonical | 1 |
| theta function identity | 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: identity in analytic number theory
Generated description
Identity in analytic number theory is a rigorously proven equality, often involving series, integrals, or arithmetic functions, that reveals structural relationships between number-theoretic objects and underpins analytic techniques such as transforms, convolutions, and explicit formulas.
Instances (4)
| Instance | Via concept surface |
|---|---|
| Jacobi triple product | q-series identity |
| Euler product formula for the Riemann zeta function | — |
| Arthur trace formula | generalization of the Selberg trace formula |
| Rogers–Ramanujan-type identities | q-series identity |