I'm studying $p$-adic analysis now and particularly $p$-adic interpolation; for example, constructions like $p$-adic $L$-functions (Kubota-Leopoldt style). I'm having some difficulty though, and I'd like to start with knowing what motivates the study. What do you really do with $p$-adic zeta functions and $L$-functions?
2026-03-28 23:55:53.1774742153
Why $p$-adically interpolate?
1.7k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ALGEBRAIC-NUMBER-THEORY
- Splitting of a prime in a number field
- algebraic integers of $x^4 -10x^2 +1$
- Writing fractions in number fields with coprime numerator and denominator
- Tensor product commutes with infinite products
- Introduction to jacobi modular forms
- Inclusions in tensor products
- Find the degree of the algebraic numbers
- Exercise 15.10 in Cox's Book (first part)
- Direct product and absolut norm
- Splitting of primes in a Galois extension
Related Questions in SPECIAL-FUNCTIONS
- Generalized Fresnel Integration: $\int_{0}^ {\infty } \sin(x^n) dx $ and $\int_{0}^ {\infty } \cos(x^n) dx $
- Is there any exponential function that can approximate $\frac{1}{x}$?
- What can be said about the series $\sum_{n=1}^{\infty} \left[ \frac{1}{n} - \frac{1}{\sqrt{ n^2 + x^2 }} \right]$
- Branch of Math That Links Indicator Function and Expressability in a Ring
- Generating function of the sequence $\binom{2n}{n}^3H_n$
- Deriving $\sin(\pi s)=\pi s\prod_{n=1}^\infty (1-\frac{s^2}{n^2})$ without Hadamard Factorization
- quotients of Dedekind eta at irrational points on the boundary
- Sources for specific identities of spherical Bessel functions and spherical harmonics
- Need better resources and explanation to the Weierstrass functions
- Dilogarithmic fashion: the case $(p,q)=(3,4)$ of $\int_{0}^{1}\frac{\text{Li}_p(x)\,\text{Li}_q(x)}{x^2}\,dx$
Related Questions in P-ADIC-NUMBER-THEORY
- How does one define an inner product on the space $V=\mathbb{Q}_p^n$?
- Can $\mathbb{Z}_2$ be constructed as the closure of $4\mathbb{Z}+1$?
- Number of points in reduction of a p-adic analytic manifold.
- How do I translate functions on the Prufer 2-group between functions on the $2^n$ roots of unity and the dyadic fractions modulo 1?
- Hensel Lemma and cyclotomic polynomial
- orbit representatives for the group of unipotent matrix acting on the set of skew-symmetric matrices
- Homomorphic images of $p$-adic integers
- Criteria for a cubic polynomial in $\Bbb Q[x]$ to split completely over $\Bbb Q_p$
- What do the elements of the affinoid algebra $A=K\langle x, y\rangle/(y-\pi x)$ look like?
- Find $\frac{a}{b} \in \mathbb{Q}$ such that $ |\,\frac{a}{b} - \sqrt{2}|_3 < \epsilon $
Related Questions in ARITHMETIC-GEOMETRY
- Showing that a Severi-Brauer Variety with a point is trivial
- Definition of scheme defined over a ring A
- Galois representation on Tate module of a twist of an elliptic curve
- What is the difference between algebraic number theory, arithmetic geometry and diophantine geometry?
- Questions about Zeta Function of Singular Plane Curve
- Brauer group of global fields
- Structure of étale maps
- Unipotent Groups and Torsors
- why is multiplication by n surjective on an abelian variety
- Poincare duality compatible with the definition of compactly supported cohomology in etale cohomology?
Related Questions in ZETA-FUNCTIONS
- What is the name of this zeta function?
- Computing the value of a spectral zeta function at zero
- Zeta regularization vs Dirichlet series
- How to locate zeros of the Riemann Zeta function?
- Where does $\pi$ of the class number formula come from?
- What can we say about class number of a number field using class number formula?
- zeta function of $A^n$?
- Calculating Values for Reimann zeta function
- Approximation of $\zeta(3)$
- Frobenius map, zeta functions of a variety over $\mathbb{F}_p$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?