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2 “.... The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when...”

3 Table of Contents: “... -- Applications: equations and sieves -- Ideal decomposition in number fields -- Reciprocity laws...”

4 Table of Contents: “... -- Sieve -- Applied Mathematics Explored -- Lost Memories -- Back to Math -- Dabbling in Mathematical...”

5 Table of Contents: “...Sieves for theorems of Euler, Rogers, and Ramanujan -- The Voronoï summation formula...”

6 “... of the Euclidean algorithm; * Infinite sets and the pioneering work of Georg Cantor; * The sieve of Eratosthenes...”

7 Table of Contents: “... decompositions of integers to probability experiments -- Chapter 3: From number sieves to difference equations...”

8 Table of Contents: “... Experiments; The Sieve of Eratosthenes: An Algorithm for Finding Prime Numbers; A Journey of a Thousand Miles...”