Archive for November, 2010

IV.2 Analytic Number Theory by Andrew Granville, Gaps Between Primes Revisited, Sieve Methods and Smooth Numbers: Pages 344 – 346.

Wednesday, November 10th, 2010

Analytic Number Theory by Andrew Granville.

Gaps Between Primes Revisited.

Sieve Methods.

Smooth Numbers.

IV.2 Analytic Number Theory by Andrew Granville, Gaps Between Primes that are Smaller than Average and Very Small Gaps Between Primes: Pages 342 – 344.

Tuesday, November 9th, 2010

Analytic Number Theory by Andrew Granville.

Gaps Between Primes that are Smaller than Average.

Very Small Gaps Between Primes.

IV.2 Analytic Number Theory by Andrew Granville, The “Analysis” in Analytic Number Theory, The Riemann Hypothesis, Primes in Arithmetic Progressions and Primes in Short Intervals: Pages 336 – 342.

Monday, November 8th, 2010

Analytic Number Theory by Andrew Granville.

The “analysis” in analytic number theory.

The Riemann hypothesis.  If 0<=Re(s)<=1, s complex and Zeta(s) = 0 then Re(s)=1/2.

Primes in arithmetic progressions.

Primes in short intervals.

IV.2 Analytic Number Theory by Andrew Granville, Bounds for the number of primes: Pages 333 – 335.

Friday, November 5th, 2010

Analytic Number Theory by Andrew Granville.

Various proofs that there are an infinite number of primes.

Bounds for the number of primes.

IV.1 Algebraic Numbers by Barry Mazur, Fields of Algebraic Numbers and Rings of Algebraic Integers, Sizes, Weil Numbers, IV.2 Analytic Number Theory by Andrew Granville: Pages 329 – 332.

Thursday, November 4th, 2010

Algebraic Numbers by Barry Mazur.

Fields of Algebraic Numbers.

Rings of Algebraic Integers.

On the size(s) of the absolute values of all conjugates of an algebraic integer.

Weil Numbers.

Epilogue.

IV.2 Analytic Number Theory by Andrew Granville.

Introduction.

Analytic number theory, as opposed to algebraic, looks for good approximations.

IV.1 Algebraic Numbers by Barry Mazur, degree, ciphers and minimal polynomials and some remarks about the theory of polynomials: Pages 328 – 329.

Monday, November 1st, 2010

Algebraic Numbers by Barry Mazur.

The degree of an algebraic number.

Algebraic numbers as ciphers determined by their minimal polynomials.

A few remarks about the theory of polynomials.