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Simon Jackson
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Decks in this class (26)
Lecture 1
What is dirichlet s theorem,
What is the prime number theorem
2
cards
Lecture 2
Define divisibility,
Give the properties of divisibility,
Define the greatest common divisor
11
cards
Lecture 3
Define arithmetical functions,
What is the mobius function,
How can we write the sum of mobiu...
9
cards
Lecture 4
Define the dirichlet product diri...,
What is the function n,
What arithmetical properties hold...
9
cards
Lecture 5
Multiplicative functions,
Completely multiplicative functions,
If f is multiplicative what is f 1
15
cards
Lecture 6
What is a generalised convolution,
If f x 0 for all nonintegral x wh...,
What restrictions do we require o...
10
cards
Lecture 7
What is the big oh notation,
What does an equation of the form...,
What does f t o g t imply for t a
14
cards
Lecture 8
Give dirichlet s asyptotic formula,
Give dirichlet s asyptotic formul...,
What is the average order of the ...
4
cards
Lecture 9
Find n x n for x 1,
What s the order of n and n,
State the partial sum of the covo...
5
cards
Lectures 10 & 11
For all x 1 we have n 1 n n 1 whe...,
Show _ n x n n 1,
Give legendre s identity
11
cards
Lectures 12 & 13
Use abel s identity to express x ...,
Use abel s identity to express x ...,
State the prime number theorem as...
6
cards
Lecture 14
Apply shapiros theorem to the von...,
N x x n find the answer using sha...,
Find the answer using shapiros th...
5
cards
Lecture 15
Lim_ x m x x 0 what is this equiv...,
M x o x as x what does this imply
2
cards
Lecture 16
If a x _ n x n n what relation im...,
Let f be a real or complex valued...
2
cards
Elementary proof of PNT
Selberg s asymptotic formula,
What are the steps for the elemen...,
In the el pr pnt what do we set x...
7
cards
Lecture 17
What is the abscissa of absolute ...,
If f n n s converges everywhere h...,
If f n n s converges nowhere how ...
4
cards
Lecture 18
Uniqueness theorem
1
cards
Lecture 19
What is an euler product,
Euler product for completely mult...,
_ n 1 f n n s if f is multiplicat...
9
cards
Lecture 20
Let fn be a sequence of functions...,
The sum function f s _ n 1 f n n ...,
Landau s theorem
3
cards
Lecture 21
Let f s f n n s be absolutely con...
1
cards
Lecture 22
Assume the series f s n 1 f n n s...,
Assume the series f s n 1 f n n s...,
Perron s formula
4
cards
Lecture 23
Riemann zeta function,
Euler product representation of r...,
Suppose that 0 x 0 and s 1 then f...
7
cards
Lecture 25 (PNT lemmas)
For any arithmetical function a n...,
Let a x n x a n and let a1 x x_1 ...,
Let a x n x a n and let a1 x x_1 ...
5
cards
Lecture 26
Give a contour integral represent...,
If c 1 and x 1 find 1 x x 2 1 2 1...,
Upper bounds for s and s near the...
3
cards
Lecture 27
If 1 what is the lower bound of 3...,
We have 1 it 0 for what t,
Inequalities for 1 s and s s
3
cards
Lecture 28
If f s has a pole of order k at s...,
The function f s s s 1 s 1 is ana...,
For x 1 we have 1 x x 2 1 2 1 1 x...
4
cards
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Analytic Number Theory
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