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Goodwill and Intangible Assets, Net
 12 Months Ended
Sep. 30, 2020
Goodwill and Intangible Assets Disclosure [Abstract]  
Goodwill and Intangible Assets, Net
Note 9 — Goodwill and Intangible Assets, Net 
The following table presents details of the Company’s total goodwill:
As of September 30, 2018
  $
2,444,895
 
Goodwill resulting from acquisitions(1)
   
17,484
 
Other
   
456
 
         
As of September 30, 2019
  $
2,462,835
 
Goodwill resulting from acquisitions(2)
   
118,628
 
Other
   
(2,818
) 
         
As of September 30, 2020
  $
2,578,645
 
         
 
(1)
Mainly relates to the acquisition of TTS. In
allocating the total purchase price for
T
TS
, based on estimated fair values, the Company recorded $8,218 of goodwill, $29,500 of customer relationships to be amortized over approximately six years, $2,100 of core technology to be amortized over approximately six years
 and
 $1,300 of trade mark to be amortized
over four years.
 
 
(2)
Mainly relates to the acquisition of Openet. In allocating the total preliminary purchase price for Openet, based on estimated fair values, the Company recorded
$102,898 of goodwill, $40,409 of customer relationships to be amortized over approximately eight years, $53,614 of core technology to be amortized over approximately five years and $2,594 of trade mark to be amortized over two years.
The Company performs an annual goodwill impairment test during the fourth quarter of each fiscal year, or more frequently if impairment indicators are present. The Company operates in one operating segment, and this segment comprises its only reporting unit. In calculating the fair value of the reporting unit, the Company uses its market capitalization and a discounted cash flow methodology. There was no impairment of goodwill in fiscal years 2020, 2019 or 2018
.
The following table presents details regarding the Company’s total definite-lived purchased intangible assets:
 
Gross
 
  
Accumulated
Amortization
 
  
Net
 
September 30, 2020
 
 
 
  
 
 
  
 
 
Core technology
   $
896,814
     $
(735,534
 )   $
161,280
  
Customer relationships
   
642,575
      
(517,670
 )    
124,905
  
Other
   
47,540
      
(37,391
 )    
10,149
  
                         
Total
  $
1,586,929
     $
(1,290,595
 )   $
296,334
  
                         
September 30, 2019
 
 
 
 
 
 
 
 
 
 
 
 
Core technology
   $
775,479
     $
(690,961
 )   $
84,518
  
Customer relationships
   
594,555
      
(483,313
 )    
111,242
  
Other
   
44,946
      
(35,544
 )    
9,402
  
                         
Total
  $
1,414,980
     $
(1,209,818
 )   $
205,162
  
                         
The amortization expenses related to the Company’s definite-lived purchased intangible assets were $80,777, $94,385 and $105,785 for the years
ended 2020, 2019 and 2018
,
respectively.
 
The estimated future amortization expense of def
i
nite-lived purchased intangible assets as of September 30, 2020 is as follows:
 
Amount
 
Fiscal year:
 
 
 
2021
  $
78,345
  
2022
   
63,819
  
2023
   
46,672
  
2024
   
38,954
  
2025
   
34,534
  
Thereafter
   
34,010
  
         
Total
  $
296,334