Note on a result of Shparlinski and related results
Tom 193 / 2020
                    
                    
                        Acta Arithmetica 193 (2020), 157-163                    
                                        
                        MSC: Primary 11B30, 11L03; Secondary 11B75.                    
                                        
                        DOI: 10.4064/aa181018-8-4                    
                                            
                            Opublikowany online: 16 January 2020                        
                                    
                                                Streszczenie
Using graph spectra, we give a new proof of a statement of Shparlinski which was the main tool in the estimation of the energy of a distance set and we derive some consequence of it. Assuming some additional condition, we give a new estimation on the energy of the distance set.
 
             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                         
                                                            