# 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.

**7**

**0**answers

### Are there natural Dirichlet series whose completions have poles in the region of absolute convergence?

**2**

**1**answer

### Watson's triple product for automorphic forms shifted by Maass rising operators

**-4**

**1**answer

### Scaled Riemann zeta function with no zero in the critical strip

**0**

**0**answers

### Is $\operatorname{Aut}(\mathcal{M})$ a fundamental group in Grothendieck's sense?

**24**

**1**answer

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

**6**

**2**answers

### Vinogradov-Korobov for Dirichlet L-functions?

**7**

**2**answers

### Functional equation and/or growth estimates for a shifted L function

**3**

**2**answers

### Distribution of zeros of real quadratic Dirichlet L-functions in small intervals

**8**

**2**answers

### Do odd-weight cusp forms have analytic rank 0?

**2**

**0**answers

### Iwasawa theory over function fields - How do eigenvalues vary in $\mathbb Z_\ell$ towers?

**0**

**1**answer

### Extending functional inequality from rectangles to parallelograms

**2**

**0**answers

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

**1**

**1**answer

### How to find an explicit value of a Hecke L-function using Magma?

**2**

**1**answer

### What's the motivation for the $3$ appearing in Iwaniec and Kowalski's definition of the analytic conductor?

**0**

**1**answer

### Why does LMFDB refer to L functions having coefficients of type $a_p-a_{p^2}$ instead of just $a_{p^2}$?

**8**

**1**answer

### Spectral decomposition of product of modular functions

**14**

**1**answer

### Bound for $GL(3)$ symmetric square

**33**

**1**answer

### The modularity theorem as a special case of the Bloch-Kato conjecture

**3**

**0**answers

### Maass--Selberg for any Eisenstein series on higher rank

**0**

**1**answer

### Are there infinitely many L-rigs?

**4**

**0**answers

### Lower bound on symmetric square L-function

**6**

**1**answer

### Which cases of Beilinson-Bloch-Kato for elliptic motives are known?

**20**

**1**answer

### Hadamard factorization of L-functions

**3**

**0**answers

### L functions of Symmetric power of elliptic curves

**1**

**0**answers

### Rankin-Selberg method and Symmetric power of elliptic curves

**8**

**1**answer

### Proof of a 'well-known' result of Shimura on periods of modular forms

**3**

**0**answers

### L functions of elliptic curves over quadratic fields

**3**

**0**answers

### On the ''generalised'' Chebyshev psi function

**1**

**0**answers

### On the error bound for the Prime Number Theorem for arithmetic progressions

**4**

**0**answers

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

**5**

**0**answers

### Twisted functional equations in Goldfeld's book

**1**

**1**answer

### Moments of Dirichlet $L$-functions on the critical line

**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

### 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?

**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

**9**

**1**answer

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

**8**

**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