The Bateman-Horn conjecture: Heuristic, history, and applications

被引：11
作者：
Aletheia-Zomlefer, Soren Laing [2 ]
Fukshansky, Lenny [1 ]
Garcia, Stephan Ramon [2 ]
机构：
[1] Claremont Mckenna Coll, Dept Math, 850 Columbia Ave, Claremont, CA 91711 USA
[2] Pomona Coll, Dept Math, 610 N Coll Ave, Claremont, CA 91711 USA
来源：
EXPOSITIONES MATHEMATICAE | 2020年 / 38卷 / 04期
关键词：
Prime number; Bateman-Horn conjecture; Primes in arithmetic progressions; Landau's conjecture; Twin prime conjecture; Ulam spiral; QUADRATIC POLYNOMIALS; CLASS-NUMBER; PRIMES; PRODUCTS; SERIES; PROOF; FORMS; GAPS;
D O I：
10.1016/j.exmath.2019.04.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Bateman-Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green-Tao theorem, along with many famous conjectures, such the twin prime conjecture and Landau's conjecture. We discuss the Bateman-Horn conjecture, its applications, and its origins. (C) 2019 Elsevier GmbH. All rights reserved.
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页码：430 / 479
页数：50
相关论文
共 85 条
[1]  
Anderson Bethany, BIRTH COMPUTER AGE I
[2]  
[Anonymous], PROBABILISTIC MOD S4
[3]  
[Anonymous], 1958, Pac. J. Math.
[4]  
Augustin D., CUNNINGHAM CHAIN REC
[5]   LINEAR FORMS IN LOGARITHMS OF ALGEBRAIC NUMBERS [J].
BAKER, A .
MATHEMATIKA, 1966, 13 (26P2) :204-&
[6]  
Bateman P.T., 1962, Math. Comput, V16, P363, DOI [10.1090/S0025-5718-1962-0148632-7, DOI 10.1090/S0025-5718-1962-0148632-7]
[7]  
Bateman P.T., 1962, Illinois J. Math., V6, P142
[8]  
BATEMAN PT, 1965, P S PURE MATH, V8, P119
[9]  
Beeger N.G. W. H., 1939, NIEUW ARCHIEF WISKUN, V20, P48
[10]  
Bombieri E., 2006, NEW MATH MONOGRAPHS, V4, P652
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