# Algebra and Number Theory Seminar Fall 2017

**September 29, 2017**

**No seminar**

**October 6, 2017**

**No seminar**

**October 13, 2017**

**Robert Boltje, University of California, Santa Cruz**

**Picard Groups of Block Algebras****October 20, 2017**

**No seminar**

**October 27, 2017 **

**Joe Ferrara, University of California, Santa Cruz**In the 1970's Stark made precise conjectures about the leading term of the Taylor series expansion at s=0 of Artin L-functions, refining Dirichlet's class number formula. Around the same time Barsky, Cassou-Nogues, and Deligne and Ribet for totally real fields, along with Katz for CM fields defined p-adic L-functions of ray class characters. Since then Stark-type conjectures for these p-adic L-functions have been formulated, and progress has been made in some cases. The goal of this talk is to discuss a new definition of a p-adic L-function and Stark conjecture for a mixed signature character of a real quadratic field. After stating the definition and conjecture, theoretical and numerical evidence will be discussed.

*A p-adic Stark Conjecture for Hecke Characters of Quadratic Fields*

**November 3, 2017**

**Edmund Karasiewicz, University of California, Santa Cruz**

** Eisenstein Series and L-functions**Automorphic forms often contain arithmetic information; for example, powers of the Jacobi theta-function encode the number of ways an integer can be represented as a sum of squares. One method of packaging this arithmetic information is in the form of an L-function; the problem of extracting this arithmetic information has become a principal problem for number theorists. We will describe some techniques that utilize Eisenstein series, particular types of automorphic forms, to prove important properties of automorphic L-functions. A particular emphasis will be placed on Eisenstein series of GL(2), GL(3), and their double covers.

**November 10, 2017**

**No Seminar**

**November 17, 2017**

**No Seminar**

**November 24, 2017**

**Holiday - No Seminar**

**December 1, 2017**

**No Seminar**

**December 8, 2017**

No Seminar

** **