# 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**

**1**answer

### Functional equation for general number fields

**-2**

**0**answers

### Are there proven cases of permutations of the Satake parameters being actually isometries ?

**2**

**0**answers

### Function equation over general number fields

**4**

**1**answer

### Modular forms and Period Polynomials

**3**

**0**answers

### holomorphic continuation of motivic $L$-functions

**1**

**0**answers

### Mean value estimates for general number fields

**7**

**1**answer

### Relation between Fourier coefficients and Satake parameters

**4**

**1**answer

### Corollary for Casselman-Shalika formula

**10**

**1**answer

### Euler factors of L-function at bad primes

**8**

**1**answer

### Analogue of the original Birch–Swinnerton-Dyer conjecture for abelian varieties

**13**

**1**answer

### BSD conjecture for rank 1 elliptic curves

**4**

**1**answer

### Local L-function $L(s,\pi_p\times \chi_p)=1$

**16**

**0**answers

### Why arithmetic Langlands?

**0**

**0**answers

### Summation formula for twisted L-function

**4**

**0**answers

### Strengthened supercongruences for Ramanujan-type formulas for $1/\pi^k$

**8**

**0**answers

### Local Langlands Correspondence for unramified principal series representations

**1**

**0**answers

### A mixed of the Dedekind zeta function and the L-function

**6**

**1**answer

### p-adic L-functions for (dual of) fine Selmer Groups

**3**

**0**answers

### L-functions for the Weil group over short exact sequences

**8**

**1**answer

### Definitions of $\pi_1 \times \pi_2, \pi_1 \boxplus \pi_2, \pi_1 \boxtimes \pi_2$

**3**

**0**answers

### Generalization of Weil's theorem for L-functions

**2**

**0**answers

### Definition of Local L-function for a representation of a torus?

**12**

**3**answers

### Some questions on the $p$-adic properties of special $L$-values

**3**

**2**answers

### What is known about gaps between zeros of L-functions?

**1**

**1**answer

### A question about Kato's explicit reciprocity law

**4**

**1**answer

### References on Erdos conjecture on arithmetic progressions

**14**

**2**answers

### What are zeta functions good for?

**10**

**1**answer

### Critical points of Dirichlet L functions

**6**

**1**answer

### Herbrand-Ribet and Mazur-Wiles for function fields

**3**

**0**answers

### L-functions and Hecke theory for general number fields

**3**

**1**answer

### Consistency of the notion of conductor of a representation

**6**

**1**answer

### Symmetric powers of Ramanujan tau-function

**6**

**1**answer

### Regulator of abelian extensions of Q

**6**

**1**answer

### The L-function of Q(-1/2) and the “number of prime $p\equiv 3$ divisors” function

**10**

**0**answers

### Infinite extensions such that every elliptic curve has finite rank

**5**

**1**answer

### Does $ M(x)=O(\sqrt{x}) $ if and only if the De Bruijn-Newman constant is negative?

**5**

**0**answers

### Relation between Gross-Koblitz and Chowla-Selberg formulas

**2**

**0**answers

### Questions about the exceptional zeros of Dirichlet $L$-functions

**6**

**1**answer

### Difference of Beilinson conjecture and equivariant Tamagawa number conjecture

**5**

**2**answers

### Can the relative degree and ramification index can be read off the characteristic polynomial?

**3**

**0**answers

### Expression of the root number for Maass forms

**-1**

**1**answer

### Which properties of L-functions can be proven assuming they are objects of a symmetric bimonoidal category?

**8**

**1**answer

### Special values of adjoint $L$-functions of automorphic representations of $\mathrm{GSp}(4)$ as Petersson norms

**4**

**1**answer

### Poles of $L$-functions associated to Maass forms

**9**

**1**answer

### How does Riemann hypothesis implies estimates?

**5**

**0**answers

### Local L-factors for automorphic representations

**3**

**1**answer

### On computing the periods for $L$-function of a primitive form for $\Gamma_0(N)$ and of weight $k > 2$

**36**

**1**answer

### A mysterious connection between Ramanujan-type formulas for $1/\pi^k$ and hypergeometric motives

**8**

**0**answers

### Residue of Eisenstein Series on GL(n)

**11**

**1**answer