p-ADIC q-HIGHER-ORDER HARDY-TYPE SUMS

Title & Authors
p-ADIC q-HIGHER-ORDER HARDY-TYPE SUMS
SIMSEK YILMAZ;

Abstract
The goal of this paper is to define p-adic Hardy sums and p-adic q-higher-order Hardy-type sums. By using these sums and p-adic q-higher-order Dedekind sums, we construct p-adic continuous functions for an odd prime. These functions contain padic q-analogue of higher-order Hardy-type sums. By using an invariant p-adic q-integral on $\small{\mathbb{Z}_p}$, we give fundamental properties of these sums. We also establish relations between p-adic Hardy sums, Bernoulli functions, trigonometric functions and Lambert series.뮧ﾖ⨀ﾖ⨀徭ﾖ⨀䥺֗⨀큾֗⨀뺀֗⨀ﾖ⨀띲֗⨀뉻֗⨀֗⨀ﾪﾖ⨀֗⨀襵֗⨀뺭ﾖ⨀嚁֗⨀覢ﾖ⨀좮ﾖ⨀湸֗⨀ᦦﾖ⨀�֗⨀⊥ﾖ⨀멸֗⨀璄֗⨀ڦﾖ⨀ﾖ⨀깳֗⨀ቾ֗⨀敹֗⨀퍱֗⨀Ңﾖ⨀솠ﾖ⨀蝱֗⨀㞩ﾖ⨀놦ﾖ⨀嚮ﾖ⨀乱֗⨀䉿֗⨀왽֗⨀ﲤﾖ⨀具֗⨀㽹֗⨀뾯ﾖ⨀֗⨀ꎃ֗⨀劦ﾖ⨀蚂֗⨀䲀֗⨀潺֗⨀㵵֗⨀䂨ﾖ⨀ギﾖ⨀֗⨀貨ﾖ⨀흹֗⨀㡾֗⨀֗⨀ⱹ֗⨀֗⨀邃֗⨀ᶁ֗⨀驱֗⨀ᆩﾖ⨀�֗⨀㪯ﾖ⨀슢ﾖ⨀튂֗⨀⹽֗⨀֗⨀ﶦﾖ⨀癵֗⨀䝶֗⨀筿֗⨀끷֗⨀犭ﾖ⨀㙺֗⨀욪ﾖ⨀㶢ﾖ⨀䲭ﾖ⨀嶩ﾖ⨀坰֗⨀㦭ﾖ⨀뾂֗⨀ﾖ⨀ಅ֗⨀쉵֗⨀鲢ﾖ⨀颭ﾖ⨀ѵ֗⨀⭷֗⨀뚃֗⨀誤ﾖ⨀靾֗⨀ᾅ֗⨀펄֗⨀᭽֗⨀⚀֗⨀扳֗⨀떁֗⨀캧ﾖ⨀֗⨀᥹֗⨀녹֗⨀ﾖ⨀➂֗⨀麦ﾖ⨀猪ﾖ⨀쒦ﾖ⨀๶֗⨀횤ﾖ⨀侠ﾖ⨀鱵֗⨀ẃ֗⨀⥳֗⨀䒃֗⨀᩻֗⨀�֗⨀걯֗⨀汴֗⨀骄֗⨀辮ﾖ⨀䆪ﾖ⨀즃֗⨀뱼֗⨀䕲֗⨀趪ﾖ⨀鍶֗⨀庫ﾖ⨀뎪ﾖ⨀ﾖ⨀�֗⨀֗⨀梬ﾖ⨀౲֗⨀⪢ﾖ
Keywords
Dedekind sums;p-adic Dedekind sums;generalized Dedeking sums;Hardy sums;Bernoulli polynomizls and functions;Lambert series p-adic q-higher order Dedekind sums;p-adic q-Bernoulli numbers;
Language
English
Cited by
1.
Special functions related to Dedekind-type DC-sums and their applications, Russian Journal of Mathematical Physics, 2010, 17, 4, 495
2.
q-Hardy–Berndt type sums associated with q-Genocchi type zeta and q-l-functions, Nonlinear Analysis: Theory, Methods & Applications, 2009, 71, 12, e377
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