p-Adic Limits of Shintani Generating Functions for a Real Quadratic Field

p-adic Deformation of Shintani Cycles

The goal of this thesis is to generalize to elliptic curves a classical formula of Hecke. This is chiefly achieved through studying p-adic deformation of certain Shintani cycles attached to a real quadratic field K and an elliptic curve E/Q of conductor N . Assume that all the prime divisors of N are split in K. Also suppose that E has multiplicative reduction at a prime p, and denote by f E th...

Computing p-adic L-functions of totally real number fields

We prove new explicit formulas for the p-adic L-functions of totally real number fields and show how these formulas can be used to compute values and representations of p-adic L-functions.

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

p-ADIC NORMS AND QUADRATIC EXTENSIONS, II

We investigate the graph theoretical aspects and combinatorics of the action of a unitary group in n variables over a local non-archimedian eld on the Bruhat-Tits building of an odd orthogonal group in 2n+ 1 variables.

Nearly Quadratic Mappings over p-Adic Fields

and Applied Analysis 3 As a special case, if n 2 in 1.3 , then we have the functional equation 1.2 . Also, if n 3 in 1.3 , we obtain 2 ∑ i1 2 3 ∑ i2 i1 1 f ⎛ ⎝ 3 ∑ i 1, i / i1,i2 xi − 2 ∑ r 1 xir ⎞ ⎠ 3 ∑ i1 2 f ⎛ ⎝ 3 ∑ i 1, i / i1 xi − xi1 ⎞ ⎠ f ( 3 ∑