On a Problem of Mordell with Primitive Roots

2009/11/15 by Cristian Cobeli, Cobeli, Cristian · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.0911.2832

7 pages, added detailed proof of Lemma 2

openalex publication_date 2009/11/15 · arxiv created 2009/12/30 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the sums of the form S=∑_x=1^N exp((ax+b₁g₁^x+... +b_rg_r^x)/p ), where p is prime and g₁,..., g_r are primitive roots \pmod p. An almost forty years old problem of L. J. Mordell asks to find a nontrivial estimate of S when at least two of the coefficients b₁,...,b_r are not divizible by p. Here we obtain a nontrivial bound of the average of these sums when g₁ runs over all primitive roots \pmod p.

Cited by

• Small Prime Primitive Roots in Arithmetic Progressions

Related

• Topics In Primitive Roots
• Simultaneous Primitive Roots over Finite Rings
• Explicit upper bounds on the least primitive root
• Character sums over shifted primes
• Exponential sums over primes are unbounded