Square root p-adic L-functions, I : Construction of a one-variable measure

p-Adic description of Higgs mechanism I: p-Adic square root and p-adic light cone

This paper is the first one in the series devoted to the calculation of particle mass spectrum in Topological GeometroDynamics. In this paper p-adic conformal field theory limit of TGD is formulated. TGD Universe is critical at quantum level and the idea is to realize criticality via conformal invariance. Ordinary real numbers do not allow this but if one assumes that in long length scales p-ad...

p-ADIC VARIATION OF L FUNCTIONS OF ONE VARIABLE EXPONENTIAL SUMS, I

For a polynomial f(x) in (Zp∩Q)[x] of degree d ≥ 3 let L(f⊗Fp;T ) be the L function of the exponential sum of f mod p. Let NP(f⊗Fp) denote the Newton polygon of L(f⊗Fp;T ). Let HP(Ad) denote the Hodge polygon of Ad, which is the lower convex hull in R2 of the points (n, n(n+1) 2d ) for 0 ≤ n ≤ d−1. Let Ad be the space of degree-d monic polynomials parameterized by their coefficients. Let GNP(A;...

p-ADIC VARIATION OF L FUNCTIONS OF ONE VARIABLE EXPONENTIAL SUMS, II

Let d ≥ 3 be an integer and p a prime coprime to d. Let Q and Qp be the algebraic closure of Q and Qp respectively. Let Zp be the ring of integers of Qp. Suppose f(x) is a degree-d polynomial in (Q ∩ Zp)[x]. Let Q(f) be the number field generated by coefficients of f in Q. Let P be a prime ideal in the ring of integers OQ(f) of Q(f) lying over p, with residue field Fq for some p-power q. Let A ...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

L-FUNCTIONS OF p-ADIC CHARACTERS

We define a p-adic character to be a continuous homomorphism from 1 + tFq [[t]] to Zp. For p > 2, we use the ring of big Witt vectors over Fq to exhibit a bijection between p-adic characters and sequences (ci)(i,p)=1 of elements in Zq , indexed by natural numbers relatively prime to p, and for which limi→∞ ci = 0. To such a p-adic character we associate an L-function, and we prove that this L-f...