Atle Selberg Collected Papers by Atle Selberg

By Atle Selberg

Best number theory books

Number Theory 1: Fermat's Dream

This is often the English translation of the unique jap ebook. during this quantity, "Fermat's Dream", center theories in glossy quantity idea are brought. advancements are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the quantity fields. This paintings provides a sublime viewpoint at the ask yourself of numbers.

Initial-Boundary Value Problems and the Navier-Stokes Equations

This publication offers an advent to the huge topic of preliminary and initial-boundary worth difficulties for PDEs, with an emphasis on functions to parabolic and hyperbolic structures. The Navier-Stokes equations for compressible and incompressible flows are taken for instance to demonstrate the consequences.

Extra info for Atle Selberg Collected Papers

Example text

In 3)1, the number of elements with at least m prime i i_ divisors in the interval x ® < p ^ x a is not exceeding -L ^ p(- - xT\ Proof. For l ^ y ^ i — s, let Fj be the subset of 2ft whose elements are divided by ps+j- Indeed, Fj is the set of integers n satisfying the following conditions: * » - * < » < x v , « # 0 ( m o d ^ , ) , l < i < s , n # 0 ( m o d pj+k), l < A < ^ - s , « = 0(mod ps+j). (5) 31 3 Evidently, the number of elements of Tj is not exceeding the number of integers satisfying the following conditions: ^ _4

1 (1922) 179-194. [2] H. Heilbronn, tiber die Verteilung der Primzahlen in Polynomen, Math. Ann. 104 (1931) 794-799. [3] G. Ricci, Su la congettura di Goldbach e la constante di Schnirelmann, Ann. della R. Scu. Normale Sup. di Pisa (2) 6 (1973) 70-115. [4] T. Nagell, Generalisation dun theoreme de Tchbycheff, J. Math. (8) 4 (1921) 343-356. [5] D. V. Widder, The Laplace Transform (Princeton Univ. Press, 1946), p. 192. [6] E. V. Chulanovski, Some estimations connected with Seiberg's new method, Dokl.

104 (1931) 794-799. [3] G. Ricci, Su la congettura di Goldbach e la constante di Schnirelmann, Ann. della R. Scu. Normale Sup. di Pisa (2) 6 (1973) 70-115. [4] T. Nagell, Generalisation dun theoreme de Tchbycheff, J. Math. (8) 4 (1921) 343-356. [5] D. V. Widder, The Laplace Transform (Princeton Univ. Press, 1946), p. 192. [6] E. V. Chulanovski, Some estimations connected with Seiberg's new method, Dokl. Akad. Nauk SSSR 43 (1948) 491-494. SCIENCE RECORD Vol. I, No. 1, 1957 MATHEMATICS ON SIEVE METHODS AND SOME OF THE RELATED PROBLEMS* WANG YUAN (3E X) Institute of Mathematics, Academia Sinica {Communicated by Prof.