# Questions tagged [riemann-zeta-function]

The Riemann zeta function is the function of one complex variable $s$ defined by the series $\zeta(s) = \sum_{n \geq 1} \frac{1}{n^s}$ when $\operatorname{Re}(s)>1$. It admits a meromorphic continuation to $\mathbb{C}$ with only a simple pole at $1$. This function satisfies a functional equation relating the values at $s$ and $1-s$. This is the most simple example of an $L$-function and a central object of number theory.

**0**

**0**answers

### Dynamics of extrema of the Landau Riemann $\xi(1/2+it)$ function

**2**

**0**answers

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

**6**

**3**answers

### Is regularization of infinite sums by analytic continuation unique?

**1**

**0**answers

### Not sure about meaning of a term in English in a French research paper

**3**

**1**answer

### Efficient boxing for a mean value in the Bombieri Iwaniec method

**1**

**1**answer

### Does this series, related to the Hasse/Ser series for $\zeta(s)$, converge for all $s \in \mathbb{C}$?

**-5**

**1**answer

### On the Absolute Value of the Riemann Zeta Function on the Critical Line [closed]

**0**

**2**answers

### What is the dirichlet series of $f(n)=\sum_{d | n}(\log d) / d$ function? [closed]

**0**

**0**answers

### On the asymptotics of the Chebyshev psi function

**1**

**1**answer

### Understanding a deduction in research paper of Sprang, Fischler and Zudilin (“Many Odd zeta values are irrational”)

**3**

**1**answer

### Unable to deduce an inequality in paper on odd zeta values of Fischler, Sprang and Zudilin

**4**

**0**answers

### What is the closed form of this integral?

**5**

**0**answers

### Explicit Formula for $n$th prime in terms of Riemann zeros?

**1**

**0**answers

### Question about proof of irrationality of $\zeta(3)$ [closed]

**1**

**0**answers

### Unable to think the reasoning behind an argument in one of Lemmas in research paper of T.Rivoal and K.Ball

**15**

**2**answers

### If $\zeta(s)=0$ with $\Re(s)=\frac{1}{2}$, is then $|\hat{\zeta}(s,3)|^2=\frac{1}{2}$?

**3**

**2**answers

### Can this quantity be expressed as $x\cdot \zeta(k)+y, x,y \in \mathbb{Q}$?

**1**

**1**answer

### Series representation for $\log(|\zeta(\frac{1}{2}+it)|)$

**0**

**1**answer

### Unable to understand an argument involving integratibility of a research paper of T. Rivoal

**8**

**1**answer

### A question on the Riemann zeta function

**-1**

**1**answer

### Any simplification of this inequality if it is true? :For $t\geq 1.22$: $|\zeta(0.5+it)|\leq 0.5 \frac{|\Gamma(0.5+it)|}{|\Gamma(-0.5+it)|}$

**0**

**0**answers

### if $\max_{z \in K} |\zeta(z+it)-f(z)|<\epsilon.$ then is this $\lim_{t\to \infty} \inf \frac {|\zeta'(z+it)|}{|f'(z)|} $ a finit limit?

**4**

**4**answers

### Does there exist a rational polynomial $P(x)\in{\mathbb Q}[x]{}$ such that $P(\zeta(s))=\zeta(P(s))$?

**-1**

**1**answer

### Unable to think how to prove a result related to prime number theorem in research paper of T.Rivoal and W.Zudilin

**0**

**0**answers

### A line integral involving $\zeta(s)$

**0**

**0**answers

### About generalized binomial theorem and Grünwald-Letnikov fractional derivative

**0**

**0**answers

### What are the best unconditional bounds for the discrete moments of $\zeta'$?

**0**

**0**answers

### Proportionality constant for the growth rate of $\zeta\left(s\right)$ along the imaginary axis

**1**

**0**answers

### On some integral involving the Liouville sum

**7**

**2**answers

### Better trigonometrical inequalities for $\zeta(s)$?

**4**

**1**answer

### A zeta function for the Klein Four group?

**4**

**0**answers

### Is finding positive integer solutions of $\zeta(a/b) = c$ equivalent to deciding the rationality of $\gamma$?

**10**

**1**answer

### Second moment estimates for $\zeta(s)$: different methods?

**7**

**0**answers

### Fully explicit version of Atkinson's formula?

**12**

**1**answer

### Error term when truncating series for $1/\zeta(s)$

**7**

**1**answer

### Why was the factor $\frac12$ introduced in the Riemann $\xi$ function?

**25**

**2**answers

### A new way of approaching the pole of the Riemann zeta function - and a new conjectured formula

**1**

**0**answers

### sum involving Riemann zeta function

**0**

**1**answer

### Looking for a fine exposition of a result of Littlewood

**1**

**0**answers

### Looking for a citation for a result of Littlewood

**3**

**0**answers

### Largest observed value of $S(t)$

**10**

**0**answers

### Bounding $1/\zeta(s)$ given RH

**2**

**0**answers

### Subsets of particular values of $\zeta'(k)$ that contain irrational numbers

**2**

**0**answers

### Multiple zeta values related to fractional calculus and an Appell polynomial sequence

**9**

**0**answers

### Can this infinite sum for the Riemann zeta function be generalised?

**-1**

**1**answer

### Does $\int_{2}^{\infty} (\pi(x)-Li(x))x^{-s-1} \mathrm{d}x$ converge on the real axis for $s>1/2$? [closed]

**1**

**0**answers

### The complex roots of $\left(\Gamma(\kappa s)+2^{1-s} \pi^{-s}\cos\left(\frac{\pi s}{2} \right)\Gamma(s)\,\Gamma(\kappa(1-s))\right)$

**2**

**1**answer

### Fourier transform of the von Mangoldt function?

**3**

**2**answers

### On the Dirichlet series for $1/\zeta(s)$ for real $s$ and the zeros of zeta

**3**

**0**answers