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Author: William A. Stein
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# University of Washington Number Theory Seminar

## Spring 2010

The UW Number Theory seminar will meet Fridays from 2:30 to 3:20 in Padelford C-401. (Note that it will be immediately followed by the Sage seminar.

## Winter 2010

The UW Number Theory seminar will meet Fridays from 2:30 to 3:20 in Padelford C-401. (Note that it will be immediately followed by the Sage seminar, whose schedule is here.

• January 8: William Stein (UW)
• Title: Using wedge products and Heegner points to define canonical subgroups of the Mordell-Weil group of an elliptic curve. See 20100104.pdf for what I'll be talking about (which has mistakes), and 2010-01-08-nts-stein.pdf for a scan of my notes.

• February 5: Ling Long (Iowa State University)
• Title: Finite index subgroups of the modular group and their modular forms

• Abstract: Among finite index subgroups of the modular group, majority of them are noncongruence; namely, they do not contain any principal congruence subgroups. By a theorem of Belyi, it is known that smooth irreducible projective algebraic curves can be realized as modular curves for finite index subgroups of the modular group. Recent study reveals that despite the lack of efficient Hecke operators modular forms for noncongruence subgroups still satisfy plenty of interesting arithmetic properties. In this talk, we will discuss several arithmetic properties of finite index subgroups of the modular group and their corresponding modular forms.
• February 26: Kevin Stueve (UW)
• Title: Computing the Prime Counting Function

• Abstract: The history of the prime counting function will be discussed, with an emphasis on the table-based method of Andrew Booker (University of Bristol), which the speaker has been working on getting in Sage. Also, some of the ideas concerning the influence of the Riemann zeta function zeros on the distribution of the primes from Patrick Demichel's "The prime counting function and related subjects" will be discussed.

1/29 - Kevin Stueve
2/5 - Ling Long
2/12 - Ralph
2/19 - Aly
2/26 - Tom B
3/5 - Robert B
3/12 - Robert M