Study on linear codes and arithmetic functions by way of zeta functions

Abstract

研究代表者publisher研究種目:基盤研究(C); 研究期間:2011~2013; 課題番号:23540034; 研究分野:数物系科学; 科研費の分科・細目:数学・代数学研究成果の概要(和文): 本研究においては, 研究代表者が以前から関係している「剰余位数分布問題」において成果が得られた. これは, 整数a (2以上で完全h乗数ではない)を固定し, 素数pに対してaのmod pでの位数D _a(p)の分布を調べる, より具体的には, D _a(p)をkで割ると1余るような素数pの自然密度を調べる問題である. この問題の拡張として, 平方剰余の条件を付加した場合(Chinen-Tamura, 2012), および, mod p のかわりにmod p q とした場合(Murata-Chinen, 2013)について成果が得られた. 研究成果の概要(英文): In this research, some results are obtained in the subject "distribution of the residual orders", in which the author has been involved. This is to investigate the distribution of D_a(p), where D_a(p) is the order of a mod p (a is an integer greater than I, which is not a h-th power and p is a prime), More precisely, the problem of determining the natural density of p such that D_a(p) is congruent to I mod k. As generalizations of this problem, we obtained some results in the case where a quadratic resisue condition is added (Chinen-Tamura, 2012), and where mod pq instead of mod p (Murata-Chinen, 2013)

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