Geodesic
Some Generalizations of Ramanujan's Sum
Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1250-1260

Voir la notice de l'article provenant de la source Cambridge University Press

Ramanujan's well known trigonometrical sum C(m, n) denned by where 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. 
Ramanathan, K. G.; Subbarao, M. V. Some Generalizations of Ramanujan's Sum. Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1250-1260. doi: 10.4153/CJM-1980-093-3
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