Conjugate variables in analytic number theory. Phase space and Lagrangian manifolds

被引:0
作者
V. P. Maslov
V. E. Nazaikinskii
机构
[1] National Research University Higher School of Economics,Ishlinsky Institute for Problems in Mechanics
[2] Russian Academy of Sciences,undefined
[3] Moscow Institute of Physics and Technology (State University),undefined
来源
Mathematical Notes | 2016年 / 100卷
关键词
arithmetic semigroup; Bose gas; entropy; volume; Lagrange multiplier; conjugate variable; Lagrangian manifold;
D O I
暂无
中图分类号
学科分类号
摘要
For an arithmetic semigroup (G, ∂), we define entropy as a function on a naturally defined continuous semigroup Ĝ containing G. The construction is based on conditional maximization, which permits us to introduce the conjugate variables and the Lagrangian manifold corresponding to the semigroup (G, ∂).
引用
收藏
页码:421 / 428
页数:7
相关论文
共 27 条
[1]  
Maslov V. P.(2016)Disinformation theory for bosonic computational media Math. Notes 99 895-900
[2]  
Nazaikinskii V. E.(2016)Bose–Einstein distribution as a problemof analytic number theory: The case of less than two degrees of freedom Math. Notes 100 245-255
[3]  
Maslov V. P.(1960)Elementary solution of inverse problems on bases of free semigroups Mat. Sb. 50 221-232
[4]  
Nazaikinskii V. E.(1949)An elementary proof of the prime-number theorem Ann. Math. l50 305-313
[5]  
Bredikhin B. M.(1917)Asymptotic formulae in combinatory analysis Proc. London Math. Soc. (2) 17 75-115
[6]  
Selberg A.(1937)On the partition function Proc. London Math. Soc. (2) 43 241-254
[7]  
Hardy G. H.(1941)( Duke Math. J. 8 335-345
[8]  
Ramanujan S.(1920)) Math. Z. 7 1-57
[9]  
Rademacher H.(1968)The distribution of the number of summands in the partitions of a positive integer Arch. Rational Mech. Anal. 28 165-183
[10]  
Erdős P.(1996)Über die Eigenwerte bei den Differentialgleichungen der mathematischen Physik Funktsional. Anal. i Prilozhen. 30 19-39