All Questions
Tagged with analytic-number-theory sieve-theory
81
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Normal Order of Distinct Prime Factor $\omega(n)$
Define $\omega(n)$ as number of distinct prime factors $n$ has, that is if $n=p_1^{a_1}... p_k^{a_k}$, then $\omega(n)=k$.
It is commonly understood that normal order of $\omega(n)$ is $\log\log(n)$, ...
- 43
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1
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Density of squares using large sieves
I am reading Serre's Lectures on the Mordell-Weil Theorem, where he specifically talks about a Large Sieve inequality and proceeds to give an example.
Theorem. (Section 12.1) Let $K$ be a number ...
- 600
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Large Sieve Inequality
I am currently delving into the Large Sieve Inequality, consulting Chapter 27 of Davenport's Multiplicative Number Theory. Having completed the chapter, I seek a deeper understanding of the practical ...
- 304
3
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1
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231
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A general theorem concerning arithmetic functions
I am self-learning An Introduction to Sieve Methods and their Applications by Alina Carmen Cojocaru & M. Ram Murty.
The authors left the proof of Proposition 9.1.1 as an exercise and I try to ...
- 907
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A general Sieve method
I am studying "Sieve Methods" by Halberstam and Richert and I'm kinda stuck. In chapter 2 "The Combinatorial Sieve", in the first chapter about a general Sieve method we want to ...
- 41
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83
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Some Sieves problems
I'm currently reading some lectures notes on Sieves Problems and I stumbled across a couple of problems I'm not able to solve. Honestly, since this is my first time I'm reading on analytic number ...
- 1,344
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27
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Help needed in deducing an inequality in a lemma in the proof of linnik's theorem.
I have been reading Sieve theory from notes of Zeev Rudnick here:http://www.math.tau.ac.il/~rudnick/courses/sieves2015.html and I have a question on page 5 of lecture 14 here: http://www.math.tau.ac....
user1060925
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2 questions in the proof of Brun Titchmarch Inequality
This question is from lecture 13 of the notes of Sieve Theory here:http://www.math.tau.ac.il/~rudnick/courses/sieves2015.html
I have 2 questions in the proof of lemma 2.2 on page 3:
Question 1 : I am ...
user775699
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1
answer
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2 questions in the theory of Counting Perfect Squares
I have been reading sieve theory from notes of zeev rudnick here :http://www.math.tau.ac.il/~rudnick/courses/sieves2015.html and in page 2 of lecture 16(http://www.math.tau.ac.il/~rudnick/courses/...
user775699
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90
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Some questions in the proof of Analytic Large Sieve
I am learning about the analytic large sieve from the lecture notes here:http://www.math.tau.ac.il/~rudnick/courses/sieves2015.html . I have some question in lecture 15:http://www.math.tau.ac.il/~...
user775699
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59
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Questions in proof of Arithmetic Large Sieve
I am studying Arithmetic Large Sieve from following notes of Zeev Rudnick:http://www.math.tau.ac.il/~rudnick/courses/sieves2015.html
I have questions in lecture 14 here: http://www.math.tau.ac.il/~...
user775699
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1
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129
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A question in proof of Linnik's Theorem in Arithmetic Large Sieve
This question is from course notes in sieve theory and I am struck on this assertion in the proof of Linnik's theorem.
Consider Page 4 of lecture 14 here: http://www.math.tau.ac.il/~rudnick/courses/...
user775699
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61
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How to estimate S(z) in Arithmetic Large Sieve
This question is part of a proof in course in Sieve Theory( http://www.math.tau.ac.il/~rudnick/courses/sieves2015.html, precisely lecture 11 and 14)and I am not able to prove this particular ...
user775699
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190
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Estimating reducible monic polynomials of degree n with integer coefficients of height of atmost N
This question is from my assignment in Sieve Theory and I am struck on it. I am following following notes on Sieve Theory: http://www.math.tau.ac.il/~rudnick/courses/sieves2015.html
Question: For a ...
user775699
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Show that number of primes $p\leq x$ so that $2p+1$ is also a prime...
This question is from assignment 4 of the following sieve theory course: http://www.math.tau.ac.il/~rudnick/courses/sieves2015.html
Question : Show that the number of primes $p\leq x$ so that $2p+1$ ...
user775699