##
**Web Page of the Ottawa-Carleton Number Theory Seminar**

#
Year 2011-2012

####
**Organizers: **

- Saban Alaca: salaca at math.carleton.ca
- Damien Roy: droy at uottawa.ca

####
** March 9, 2012, 2:15-3:15pm, Room TBA **

**Speaker:** Damien Roy (U. of Ottawa)
**Title:**On the effective Lindemann-Weierstrass theorem
**Abstract:**The Lindemann-Weierstrass theorem is one of the most satisfying result of transcendental number theory. It can be stated in the following two equivalent forms:
- the exponentials of distinct algebraic numbers are linearly independent over Q,
- the exponentials of Q-linearly independent algebraic numbers are algebraically independent over Q.

Most proofs establish (1.), following the method of Hermite and its extensions by Lindemann and Weierstrass, based on the constructions of Padé approximants. The goal of this talk is to present a new simple proof of (2.) using only tools of algebraic independence (basically resultants). It leads to a measure of algebraic independence that is comparable although weaker than the best known one by Alain Sert (1999).

####
** March 16, 2012, 3:30-4:30pm, U. of Ottawa, colloquium room (585 King Edward, KED B-005) **

**Speaker:** Shabnam Akhtari (CRM)
**Title:** TBA
**Abstract:**
TBA

####
** March 23, 2012, 2:30-3:30pm, Carleton U., MacPhail Room (4351 Herzberg)**

**Speaker:**Matthew Greenberg (University of Calgary and Tutte Institute for Mathematics and Computing)
**Title:** Quaternion algebras and special value formulas
**Abstract:**
Many of the "holy grail" conjectures of number theory, e.g., the conjecture of Birch& Swinnerton-Dyer and its generalizations, describe the arithmetic content of special values of (derivatives of) L-functions at critical arguments. Although expressible as absolutely convergent Dirichlet series in right half-planes, critical arguments of interest often lie outside this half plane, and are thus defined by analytic continuation. Regardless, explicit formulas for the corresponding special values are known in many cases. In this talk, I will describe the origin and application of such formulas for L-functions of elliptic modular forms. Perhaps surprisingly, these formulas are often not given in terms of the elliptic modular forms themselves, but rather in terms of related forms, automorphic for groups of units in more general quaternion algebras. This is an instance of the "Langlandsian" philosophy that, in order to understand automorphic representations of a group, we must by necessity also understand representations on closely related groups.

####
** Seminars from previous years **