The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying 1561 – 1580 of 3028

Showing per page

On the average behavior of the Fourier coefficients of j th symmetric power L -function over certain sequences of positive integers

Anubhav Sharma, Ayyadurai Sankaranarayanan (2023)

Czechoslovak Mathematical Journal

We investigate the average behavior of the n th normalized Fourier coefficients of the j th ( j 2 be any fixed integer) symmetric power L -function (i.e., L ( s , sym j f ) ), attached to a primitive holomorphic cusp form f of weight k for the full modular group S L ( 2 , ) over certain sequences of positive integers. Precisely, we prove an asymptotic formula with an error term for the sum S j * : = a 1 2 + a 2 2 + a 3 2 + a 4 2 + a 5 2 + a 6 2 x ( a 1 , a 2 , a 3 , a 4 , a 5 , a 6 ) 6 λ sym j f 2 ( a 1 2 + a 2 2 + a 3 2 + a 4 2 + a 5 2 + a 6 2 ) , where x is sufficiently large, and L ( s , sym j f ) : = n = 1 λ sym j f ( n ) n s . When j = 2 , the error term which we obtain improves the earlier known result.

Currently displaying 1561 – 1580 of 3028