- 6 Hecke operators Recall the conjecture of Ramanujan that (mn) = (m)(n) for m, n relatively prime. While this
- 5 Dimensions of spaces of modular forms As indicated in the introduction and the last chapter, we would like to know that a given space of
- Martin, K., and D. Whitehouse. (2008) "Central L-values and Toric Periods for GL(2)," International Mathematics Research Notices, Vol. 2009, No. 1, pp. 141191
- 4.1 Reduction theory Let Q(x, y) = ax2 + bxy + cy2 be a binary quadratic form (a, b, c Z). The discriminant of Q is
- A BRIEF INTRODUCTION TO CODING THEORY KIMBALL MARTIN
- REPRESENTATIONS OF S 3 ; A 4 AND S 4 KIMBALL MARTIN
- 7 Quadratic Integers In the last chapter, we used unique factorization in Z[i] to study sums of squares. Here we give a
- 7 L-functions One of the main themes in modern number theory, is to associate to various objects (number fields,
- The first part 1 Number Fields
- Introduction to Number Theory (Fall 2009) Lecture 1: What is number theory?
- 3 Zeta and L-functions In this section we will use analytic methods to (i) develop a formula for class numbers, and (ii)
- A RELATIVE TRACE FORMULA FOR A COMPACT RIEMANN KIMBALL MARTIN, MARK MCKEE, AND ERIC WAMBACH
- TRANSFER FROM GL(2, D) TO GSp(4) KIMBALL MARTIN
- My thesis for the layman Kimball Martin
- A SYMPLECTIC CASE OF ARTIN'S CONJECTURE Kimball Martin
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
- A brief overview of modular and automorphic forms Kimball Martin
- Research in Designs & Codes Kimball Martin
- Modular Forms Spring 2011 Notes
- 2 Elliptic functions Before we introduce modular forms, which, as explained in the introduction, are functions on the
- 3 The Poincar upper half-plane There are two basic kinds of non-Euclidean geometry: spherical and hyperbolic. Spherical geometry
- [Ahl78] Lars V. Ahlfors. Complex analysis. McGraw-Hill Book Co., New York, third edition, 1978. An introduction to the theory of analytic functions of one complex variable, International
- 10.1 The ring axioms Definition 10.1. Let R be a set with two binary operations, addition + : R R R and multipli-
- The presentation here is somewhat different than the text. In particular, the sections do not match We have seen issues with the failure of unique factorization already, e.g., Z[
- Number Theory II Spring 2010 Notes
- Number Theory II Spring 2010 Notes
- 2 Primes in extensions This chapter is about the following basic question: given an extension of number fields L/K and
- 5 Non-unique factorizations In this chapter we briefly discuss some aspects of non-unique factorization, ending with an applica-
- In this, the final part of the course, we will introduce the notions of local and global viewpoints of number theory, which began with the notion of p-adic numbers. (p as usual denote a rational prime.)
- 7 Quadratic forms in n variables In order to understand quadratic forms in n variables over Z, one is let to study quadratic forms
- Adles and idles were introduced in the early 20th century as an approach to class field theory, which may be viewed as a vast generalization of quadratic reciprocity. First we introduce the notion
- Linear Algebra (MATH 3333 --04) Spring 2011 Bonus Project--Ranking Sports Teams
- Linear Algebra (MATH 3333) Spring 2011 Section 4 Midterm Practice Problems
- A Note on Difference Sets with Group Characters \Lambda Kimball Martin
- Group Theory/Number Theory Modularity of Hypertetrahedral Representations
- 9 Quadratic Reciprocity 9.1 Primes x2
- 2 The Euclidean algorithm Do you understand the number 5? 6? 7? At some point our level of comfort with individual
- CENTRAL L-VALUES AND TORIC PERIODS FOR GL(2) KIMBALL MARTIN AND DAVID WHITEHOUSE
- Shalika periods on GL2(D) and GL4 Herve Jacquet and Kimball Martin
- As needed, I will periodically update these references throughout the semester. [BorevichShafarevich] Borevich, A. I.; Shafarevich, I. R. Number theory. Translated from the Russian by Newcomb
- 12 Prime ideals Again, the presentation here is somewhat different than the text. In particular, the sections do not
- Introduction to Number Theory (Fall 2009) Kimball Martin
- 4 Modular Forms 4.1 Modular curves and functions
- 3 Congruence arithmetic 3.1 Congruence mod n
- Central L-values and periods for GL(2) Kimball Martin
- NON-UNIQUE FACTORIZATION AND PRINCIPALIZATION IN NUMBER FIELDS
- LANGLANDS CONJECTURE IN THE TETRAHEDRAL AND OCTAHEDRAL CASES KIMBALL MARTIN
- 5 The Pell equation 5.1 Side and diagonal numbers
- ON CENTRAL CRITICAL VALUES OF THE DEGREE FOUR L-FUNCTIONS FOR GSp (4): THE FUNDAMENTAL LEMMA. II
- 6 The Gaussian integers 6.1 Z[i] and its norm
- Linear Algebra (MATH 3333) Spring 2011 Section 4 Midterm Practice Problem Solutions
- 1 Background Material First we will review some basic information about p-adic fields. This is a modified version of the
- Automorphic Representations Fall 2011 Notes
- 2 Smooth Representations In this section we will introduce some basic notions and results on representations of certain topo-
- Probability (MATH 4733 -01) Fall 2011 Exam 2 -Practice Problems
- Probability (MATH 4733 -01) Fall 2011 Bonus Problem Set
- Probability (MATH 4733 -01) Fall 2011 Exam 2 -Practice Problems: Selected answers
- 3 A summary of local representation theory for GL(2) All representations from now on will be on a complex vector space. Some references are Gel-
- Notes on the Cramer-Rao Inequality Kimball Martin
- On Central Critical Values of the Degree Four L-functions for GSp (4)
- A RELATIVE TRACE FORMULA FOR A COMPACT RIEMANN KIMBALL MARTIN, MARK MCKEE, AND ERIC WAMBACH
