Almost Periodicity and the Representation of Integers as Sums of Squares

1940 ◽  
Vol 62 (1/4) ◽  
pp. 122 ◽  
Author(s):  
M. Kac
Keyword(s):  
Sums Of Squares ◽  
Almost Periodicity ◽  
Representation Of Integers

Some Generalizations of Ramanujan's Sum

1980 ◽  
Vol 32 (5) ◽  
pp. 1250-1260 ◽  
Author(s):  
K. G. Ramanathan ◽  
M. V. Subbarao
Keyword(s):  
Algebraic Number ◽  
Number Fields ◽  
Sums Of Squares ◽  
Modular Functions ◽  
Algebraic Number Fields ◽  
Representation Of Integers ◽  
Ramanujan’S Sum ◽  
Image Position ◽  
Ramanujan's Sum

Ramanujan's well known trigonometrical sum C(m, n) denned bywhere x runs through a reduced residue system (mod n), had been shown to occur in analytic problems concerning modular functions of one variable, by Poincaré [4]. Ramanujan, independently later, used these trigonometrical sums in his remarkable work on representation of integers as sums of squares [6]. There are various generalizations of C(m, n) in the literature (some also to algebraic number fields); see, for example, [9] which gives references to some of these. Perhaps the earliest generalization to algebraic number fields is due to H. Rademacher [5]. We here consider a novel generalization involving matrices.

scholarly journals Towards a computational proof of Vizing's conjecture using semidefinite programming and sums-of-squares

2021 ◽  
Vol 107 ◽  
pp. 67-105
Author(s):  
Elisabeth Gaar ◽  
Daniel Krenn ◽  
Susan Margulies ◽  
Angelika Wiegele
Keyword(s):  
Semidefinite Programming ◽  
Sums Of Squares

scholarly journals (ω, c)- Pseudo almost periodic distributions

2020 ◽  
Vol 7 (1) ◽  
pp. 237-248 ◽  
Author(s):  
Mohammed Taha Khalladi ◽  
Abdelkader Rahmani
Keyword(s):  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Differential Systems ◽  
Schwartz Distributions ◽  
Pseudo Almost Periodic Solutions ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
Pseudo Almost Periodicity ◽  
Pseudo Almost Periodic

AbstractThe paper is a study of the (w, c) −pseudo almost periodicity in the setting of Sobolev-Schwartz distributions. We introduce the space of (w, c) −pseudo almost periodic distributions and give their principal properties. Some results about the existence of distributional (w, c) −pseudo almost periodic solutions of linear differential systems are proposed.

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