# PANTS VII

## Palmetto Number Theory Seminar, Meeting 7

## College of Charleston, Charleston, SC

## October 11-12, 2008

### Information

The Palmetto Number Theory Seminar was organized in 2006 by number
theorists in
South Carolina for the purpose of fostering collaboration among us and
bringing the latest techniques and results to South Carolina through
outside speakers. PANTS is supported by grants from the NSA and
the NSF.

The upcoming meeting is being hosted by James Carter and Paul
Young at the College of Charleston.

### Plenary Speaker: Florian Luca, "On sums of powers of primes"

Abstract: All integers are divisible by the product of their
prime factors. Some, like 30, are not prime powers yet are also
divisible by the sum of their prime factors. In this talk, we will take
a closer look at such integers as well as at integers satisfying
related divisibility conditions. For example, we will see that for
every positive integer k
there are infinitely many positive integers n having more than two distinct
prime factors and which are divisible by the sum of their prime
factors, by the sum of the squares of their prime factors, and so on up
to the sum of the k-th powers
of their prime factors. The proofs use variations of Vinogradov's Three
Primes Theorem.

Many of the results presented in the talk have been obtained jointly
with Jean-Marie De Koninck.

### Plenary Speaker: Ram Murty, "L-series
and transcendental
numbers"

Abstract: We will discuss the transcendence of special values
of Hecke and Artin L-series.
We will apply this study to
obtain new results about transcendental values of the classical
Gamma function.

Contributed Talks:

James Carter, College of Charleston, An update on the restricted
Hilbert-Speiser and Leopoldt field properties

Hester Graves, University of Michigan, Introduction to Euclidean Ideal Classes

Renling Jin, College of Charleston, Plünnecke's inequality for densities

Sebastian Pauli, University of North Carolina, Greensboro, Factoring polynomials over local fields

Guohua Peng, Sichuan University, The
genus fields of function fields

Ethan Smith, Clemson University, The mean square error for the Čebotarev
Theorem in cyclotomic extensions

Jim Stankewicz, University of Georgia, Possible torsion subgroups of CM elliptic
curves

Dan Yasaki, University of North Carolina, Greensboro, Perfect forms over real quadratic fields

Paul Young, College of Charleston, Questions
related to the factorization of degenerate Bernoulli numbers

- Saturday: Florian Luca's talk at 1:00 pm, contributed talks
until
approximately 5:00 pm

- Sunday: Ram Murty's talk at 9:00 am, contributed
talks until
approximately noon

### Directions

PDF map of downtown Charleston and
Area Map If you zoom in about 200% to 300% on the downtown
map you can
see the street names listed.

Campus Map
All talks will be in room 235 of the Robert Scott Small Building, which
is building
number 23 on this map. Also note that Coming Street is a
one-way street directed away
from downtown (i.e., "Coming is going").

### Parking

Parking lots AD (entrance from Pitt Street) and GL (entrance from
George Street) are freely available on weekends. You may also
park in one of the parking garages at an hourly rate.

### Lodging

We have arranged blocks of rooms at the following Charleston
hotels. Mention that you are with PANTS. You might also
want to try http://www.hotelscombined.com/City/Charleston_South_Carolina.htm
for deals on local hotels; there is aso a rebate program for students
and educators at http://www.hotelscombined.com/Education_Support
which you may use. You can also
try hotels.com if you wish.

Best Western Sweetgrass Inn
http://www.thesweetgrassinn.com
1540 Savannah Highway, Charleston (about 7
miles from C of C), (843)571-6100, fax
(843)766-6261.
20 rooms reserved at conference rate of $139.99 if booked by September
10,
group name C of C Math Dept.

Sleep Inn Charleston
http://www.choicehotels.com
1524 Savannah Highway, Charleston (about 7
miles from C of C), (843)556-6959 or 1-877-424-6423.
20 rooms reserved at conference rate of $139.99 if booked by September
10,
group name PANTS.

Holiday Inn Express
http://www.hiexpress.com/chs-us17south
1943 Savannah Highway, Charleston (about 7
miles from C of C), (843)402-8300.
10 rooms reserved at conference rate of $139.99 if booked by September
10,
group name CMM.

### Travel Support

PANTS has a limited budget from which to provide support for
travel. Here is a visitor
expense form which may be used to request support.

### Giving a Talk

Send email to Paul Young (paul@math.cofc.edu) with your name, title (if
known), and abstract (if available). Contributed talks are
typically
twenty
minutes in length; we will attempt to accomodate talks of other
lengths.

Back to Paul's Homepage