# Questions tagged [zeta-functions]

Zeta functions are typically analogues or generalizations of the Riemann zeta function. Examples include Dedekind zeta functions of number fields, and zeta functions of varieties over finite fields. They are typically initially defined as formal generating functions, but often admit analytic continuations.

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### Schemes with common zeta function

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### Update on “A Mad day's work” by Cartier

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### Riemann-Siegel formula for Dirichlet characters

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### On integral relating logarithmic of absolute value of Zeta function:

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### Dedekind Zeta functions of Biquadratic fields

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### Why is the regulator of the degree 11 extension of $\mathbb{Q}$ so large?

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### Contemporary introduction to Godement-Jacquet “Zeta functions of simple algebras”

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### Relation between Schanuel's theorem and class number equation

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### Serge Lang's proof of Brauer-Siegel theorem

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### Summation form of the Hasse-Weil zeta function?

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### Class of differentiated Gamma functions: are there any algebras where they are elementary?

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### The zeta regularization of $\prod_{m=-\infty}^\infty (km+u)$

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### The Guinand-Weil explicit formula for Hecke characters

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### Is this closed-form summation a special case of known Lerch zeta function formulas?

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### Value of $\zeta(3/2)$?

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### Are there any zeta functions with concurrent derivative shifts in multiple variables?

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### Computing Hodge numbers by point counting

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### Riemann hypothesis for exponential sum

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### For which number fields we know the nonexistence of Stark zeros?

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### Regularity properties of Minakshisundaram–Pleijel zeta function

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### Ihara zeta function and closed paths and trails

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### Honda-Tate theorem and prescribing roots of $L$-functions

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### Deformations of the Riemann zeta function

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### Are there any extensive treatments on rational zeta series?

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### On $L$-function of permutation representation

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### Less fundamental applications of Zeta regularization:

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### On existence of conjecture relating prime zeta function:

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### Regularizing the sum of all primes

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### What's the meaning of the nontrivial zeros of Selberg zeta function?

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### Could a motivic spectrum have a “zeta function”?

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### Characterization of turning points for the Ramanujan's zeta function in the spirit of a definition by Arias de Reyna and van de Lune

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### A principle around the Ramanujan's zeta function in short intervals

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### Zeros of partial sums of the Ramanujan's zeta function

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### Prove duality of multiple zeta values by Extended Double Shuffle Relations

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### How do functional equations for zeta functions arise from the structure of a homology group?

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### A generalization of gamma function

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### The local zeta-functions of some cubic plane curves

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### Implementing zeta functions of algebraic varieties in SAGE

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### Books on complex analysis for self learning that includes the Riemann zeta function?

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### Can the corollary of the Ihara–Bass formula be extended to $ u^2 = 1 $?

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### What is the current fastest method to calculate Lerch's Phi transcendent?

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### How to measure how much a rational function/a singularity of variety is complicated?

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### Functional Equation of Zeta Function on Statistical Model

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### Igusa zeta functions of univariate polynomials: $\mathbb{Z}_p$ or $\mathbb{Q}_p$ in this statement

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### Riemann Hypothesis, Primes and Groups

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### Word length zeta function

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### Results in an article by Siegel

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### Motivation for zeta function of an algebraic variety

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### Is there research on the special values of the zeta function outside the integers?

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