Random process generated by the incomplete Gauss sums

AKARSU DEMİRCİ, Emek

Random process generated by the incomplete Gauss sums

Emek AKARSU DEMİRCİ (Recep Tayyip Erdoğan Üniversitesi, Fen Edebiyat Fakültesi, Matematik, Bölümü, Rize, Türkiye)

Turkish Journal of Mathematics

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Yıl: 2015 Cilt: 39 Sayı: 4 Sayfa Aralığı: 527 - 537 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Random process generated by the incomplete Gauss sums

Öz:

In this paper we explore a random process generated by the incomplete Gauss sums and establish an analogue ofweak invariance principle forthese sums. We focusour attentionexclusively on ageneralizationofthe limit distribution of the long incomplete Gauss sums given by the family of periodic functions analyzed by the author and Marklof.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Cellarosi F. Limiting curlicue measures for theta sums. Ann Inst Henri Poincar´e Probab Stat 2011; 47: 466497.
[2] Demirci Akarsu E, Marklof J. The value distribution of incomplete Gauss sums. Mathematika 2013; 59: 381398.
[3] Demirci Akarsu E. Short incomplete Gauss sums and rational points on metaplectic horocycles. Int J Number Thr 2014; 10: 15531576.
[4] Evans R, Minei M, Yee B. Incomplete higher order Gauss sums. J Math Anal Appl 2003; 281: 454476.
[5] Fiedler H, Jurkat WB, K¨orner O. Asymptotic expansions of ﬁnite theta series. Acta Arith 1977; 32: 129146.
[6] Jurkat WB,van Horne JW. The proof of the central limit theorem for theta sums. Duke Math J 1981; 48: 873885.
[7] Jurkat WB, van Horne JW. On the central limit theorem for theta series. Michigan Math J 1982; 29: 6567.
[8] Jurkat WB, van Horne JW. The uniform central limit theorem for theta sums. Duke Math J 1983; 50: 649666.
[9] Lehmer DH. Incomplete Gauss sums. Mathematika 1976; 23: 125135.
[10] Marklof J. Limit theorems for Theta sums. Duke Math J 1999; 97: 127153.
[11] Montgomery HL, Vaughan RC, Wooley TD. Some remarks on Gauss sums associated with kth powers. Math Proc Cambridge Philos Soc 1995; 118: 2133.
[12] Oskolkov KI. On functional properties of incomplete Gaussian sums. Canadian J Math 1991; 43: 182212.
[13] Paris RB. An asymptotic approximation for incomplete Gauss sums. J Comput Appl Math 2005; 180: 461477.
[14] Paris RB. An asymptotic approximation for incomplete Gauss sums II. J Comput Appl Math 2008; 212: 1630.

APA	AKARSU DEMİRCİ E (2015). Random process generated by the incomplete Gauss sums. , 527 - 537.
Chicago	AKARSU DEMİRCİ Emek Random process generated by the incomplete Gauss sums. (2015): 527 - 537.
MLA	AKARSU DEMİRCİ Emek Random process generated by the incomplete Gauss sums. , 2015, ss.527 - 537.
AMA	AKARSU DEMİRCİ E Random process generated by the incomplete Gauss sums. . 2015; 527 - 537.
Vancouver	AKARSU DEMİRCİ E Random process generated by the incomplete Gauss sums. . 2015; 527 - 537.
IEEE	AKARSU DEMİRCİ E "Random process generated by the incomplete Gauss sums." , ss.527 - 537, 2015.
ISNAD	AKARSU DEMİRCİ, Emek. "Random process generated by the incomplete Gauss sums". (2015), 527-537.

APA	AKARSU DEMİRCİ E (2015). Random process generated by the incomplete Gauss sums. Turkish Journal of Mathematics, 39(4), 527 - 537.
Chicago	AKARSU DEMİRCİ Emek Random process generated by the incomplete Gauss sums. Turkish Journal of Mathematics 39, no.4 (2015): 527 - 537.
MLA	AKARSU DEMİRCİ Emek Random process generated by the incomplete Gauss sums. Turkish Journal of Mathematics, vol.39, no.4, 2015, ss.527 - 537.
AMA	AKARSU DEMİRCİ E Random process generated by the incomplete Gauss sums. Turkish Journal of Mathematics. 2015; 39(4): 527 - 537.
Vancouver	AKARSU DEMİRCİ E Random process generated by the incomplete Gauss sums. Turkish Journal of Mathematics. 2015; 39(4): 527 - 537.
IEEE	AKARSU DEMİRCİ E "Random process generated by the incomplete Gauss sums." Turkish Journal of Mathematics, 39, ss.527 - 537, 2015.
ISNAD	AKARSU DEMİRCİ, Emek. "Random process generated by the incomplete Gauss sums". Turkish Journal of Mathematics 39/4 (2015), 527-537.