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Topics in Algebra and Geometry

This class was created by Brainscape user Laura Ellis. Visit their profile to learn more about the creator.

By: Laura Ellis
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Decks in this class (19)

1. The Modular Group and its Action on the Upper Half Plane
Define the group g,
Define the group,
Define the group gl2 z
13  cards
2. Modular Forms
Define a weakly modular function ...,
Define a meromorphic function on ...,
Define a meromorphic modular form...
15  cards
3. The Eisenstein Series and the Discriminant Function
Define the eisenstein series of w...,
State the power function,
Relate the riemann zeta function ...
13  cards
4. Valence Formula, Structure Theory and Dimension Formula
For meromorphic function f and po...,
For meromorphic function f and po...,
State the valence or k 12 formula
12  cards
5. Modular Forms of Congruence Subgroups
Define the principal congruence s...,
Define the hecke congruence subgroup,
Define a congruence subgroup
9  cards
6. Theta Series
Define the fourier transform f y ...,
Give the poisson summation formula,
Define the jacobi theta series
8  cards
7. L-functions
Define the riemann zeta function s,
Where does,
Define the euler product of s
14  cards
8. Hecke Theory
Define a hecke operator,
What conditions must the hecke op...,
How can we relate the q coefficie...
8  cards
T2. 1. Introduction
State prime number theorem,
What does it mean for f x g x,
State dirichlet s theorem
6  cards
T2: 2. Chebyshev's Estimates
State the formula for the power o...,
Give chebyshev s initial statement,
State the von mangoldt function
7  cards
T2. 3. Review of Complex analysis
Define the complex derivative of ...,
Define a holomorphic function on d,
Define entire for a function
11  cards
T2. 4. Perron's formula
Define a dirichlet series,
Define the abscissa of absolute c...,
Relate the abscissa of absolute a...
4  cards
T2. 5. Estimates for ζ and PNT
Define the analytic continuation ...,
Define the analytic continuation ...
2  cards
T2. 7. Arithmetic Functions
Define arithmetic functions,
Define the dirichlet convolution ...,
State the outcome 1 11 what impli...
12  cards
T2. 8. Average orders
0  cards
T2. 9. Dirichlet Characters
Define a dirichlet character,
Give the homomorphism condition o...,
Define the principle character
12  cards
T2. 10. Dirichlet L-Functions
Define the dirichlet l function f...,
Write the dirichlet l function in...,
How does the dirichlet l function...
3  cards
T2: 6. The Functional equation for ζ
0  cards
Last min T2
How do we define the meromorphic ...,
Write the functional equation for...,
Define the
15  cards

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Topics in Algebra and Geometry

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