TAILIEUCHUNG - Random process generated by the incomplete Gauss sums

In this paper we explore a random process generated by the incomplete Gauss sums and establish an analogue of weak invariance principle for these sums. We focus our attention exclusively on a generalization of the limit distribution of the long incomplete Gauss sums given by the family of periodic functions analyzed by the author and Marklof. | Turk J Math (2015) 39: 527 – 537 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Random process generated by the incomplete Gauss sums ˙ Emek DEMIRC I˙ AKARSU∗ Department of Mathematics, Faculty of Arts and Sciences, Recep Tayyip Erdo˘ gan University, Rize, Turkey • Received: • Accepted/Published Online: Printed: Abstract: In this paper we explore a random process generated by the incomplete Gauss sums and establish an analogue of weak invariance principle for these sums. We focus our attention exclusively on a generalization of the limit distribution of the long incomplete Gauss sums given by the family of periodic functions analyzed by the author and Marklof. Key words: Gauss sums, random process 1. Introduction In the present paper we deal with the curves [0, 1] → C t 7→ Xq (t) = ∑[qt] 2 h=1 eq (ph ) + (qt − [qt])eq (ph2 ) h=[qt]+1 () 2πix/q where q ∈ N , p ∈ Z× . We consider p random uniformly q = {p ≤ q

• Toán học
• Gauss sums
• Random process
• Random process generated
• Invariance principle
• Quadratic nonresidue