# Questions tagged [l-functions]

Questions about generalizations of the Riemann Zeta function of arithmetic interest whose definition relies on meromorphic continuation of special kinds of Dirichlet series, such as Dirichlet L-functions, Artin L-functions, elements of the Selberg class, automorphic L-functions, Shimizu L-functions, p-adic L-functions, etc.

**5**

**0**answers

### Non-vanishing of L-values for twists of Hilbert modular forms

**0**

**1**answer

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

**0**

**1**answer

### Logarithms of $L$-functions of irreducible characters of Galois group

**3**

**1**answer

### English reference for the Brauer-Kuroda formula

**-2**

**0**answers

### How to prove that $\mathrm{Aut}(\mathcal{M})\cong\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$?

**2**

**0**answers

### The definition of Langlands' L-function $L(s,\pi,r)$ in the case of $\operatorname{GL}_1$

**6**

**2**answers

### Analytic equivalents for primes in arithmetic progressions

**4**

**0**answers

### Small values of $L(\frac{1}{2}, \chi_{-8d})$

**1**

**1**answer

### Under Ramanujan conjecture, is primitivity equivalent to cuspidality and irreducibility?

**3**

**3**answers

### Functional derivatives on Banach spaces

**3**

**0**answers

### Is an automorphic form of $\operatorname{GL}_{n}(\mathbb{A}_{\mathbb{Q}})$ determined by its L-function?

**0**

**0**answers

### Sets of L-functions being “almost bimonoids”

**2**

**0**answers

### Relations between spectral parameters of automorphic representations

**6**

**1**answer

### “Sub-logarithmic” zero-free regions from Deuring-Heilbronn/Linnik's repulsion theorem

**4**

**1**answer

### Is the imaginary part of $t\mapsto\zeta(1/2+it)$ close to the derivative of its real part?

**3**

**0**answers

### Proving that central zero of an L-function is multiple

**8**

**1**answer

### Are the L-functions of a normalized newform and the corresponding cuspidal representation equal?

**6**

**1**answer

### Does the symmetric square L-function vanish at one?

**5**

**1**answer

### Proving automorphy of the Galois representations of number fields without considering the residual representation

**2**

**2**answers

### Upper bound of summation $\sum_{m < \frac{1}{2}X} \frac{|a(m_1m_2^2)|}{m_1m_2^2} \log\frac{X}{m}$

**4**

**2**answers

### How to compute poles and values of L-functions?

**2**

**0**answers

### Sum of inverses of zeros of $L$-functions

**12**

**1**answer

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

**2**

**1**answer

### Modular symbols associated to Rankin Selberg convolutions and the symmetric square

**4**

**0**answers

### Archimedean L-factors for symplectic group

**4**

**2**answers

### $B(\chi), L'(1,\chi)/L(1,\chi),\dotsc$

**4**

**1**answer

### Effective, explicit bound on $L'(1,\chi)/L(1,\chi)$

**9**

**1**answer

### Status of the extended form of the Lichtenbaum conjecture

**1**

**0**answers

### Mixed Hodge structures over $F\otimes \mathbb{R}$

**2**

**1**answer

### Calculation of Tate epsilon factor in the ramified case

**2**

**1**answer

### Voronoi formula for the symmetric $L$-function with level $N $

**15**

**5**answers

### $|L'(1,\chi)/L(1,\chi)|$

**4**

**0**answers

### Kronecker limit formula, modular curves, and the class number problem

**11**

**3**answers

### Are L-functions uniquely determined by their values at negative integers?

**6**

**1**answer

### Change of variables for $p$-adic integral

**3**

**2**answers

### Explicit formula: explicit work with general smoothing?

**3**

**0**answers

### Similarity between two $L$-functions (Hasse-Weil $L$-function of twisted ellptic curve and Dirichlet $L$-function)

**2**

**1**answer

### Complex L-functions for Hermitian modular forms?

**4**

**0**answers

### Is there a converse to Vatsal's theorem on congruence of p-adic L-functions?

**2**

**0**answers

### Adelic Mellin transform with nontrivial character

**2**

**0**answers

### Well-known estimate for $L(s,\chi)$ for $\sigma=\text{Re}s\geq 1/2$

**10**

**1**answer

### Least quadratic residue under GRH: an explicit bound

**4**

**2**answers

### Real non trivial zeros of Dirichlet L-functions

**4**

**0**answers

### Second derivative at 1 of L function of elliptic curve

**5**

**2**answers

### Asymptotic's for Fourier coefficients of $GL(3)$ Maass forms

**7**

**0**answers

### A mysterious number related to Hasse-Weil L-function of elliptic curve

**4**

**0**answers

### How many exceptional conductors are there?

**7**

**1**answer

### Functional equation for general number fields

**2**

**0**answers

### Function equation over general number fields

**4**

**1**answer