Upper bounds for cyclotomic numbers

• المؤلفون الرئيسيون: Duc, Tai Do, Leung, Ka Hin, Schmidt, Bernhard
• مؤلفون آخرون: School of Physical and Mathematical Sciences
• التنسيق: مقال
• اللغة: English
• منشور في: 2020
• الموضوعات: Science::Mathematics; Finite Fields; Cylotomic Fields
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/145013

Let q be a power of a prime p, let k be a nontrivial divisor of q−1 and write e=(q−1)/k. We study upper bounds for cyclotomic numbers (a,b) of order e over the finite field Fq. A general result of our study is that (a,b)≤3 for all a,b∈Z if p>(14−−√)k/ordk(p). More conclusive results will be obtai...