Exponential sums over primes formed with coefficients of primitive cusp forms

2009 ◽  
Vol 25 (4) ◽  
pp. 687-692
Author(s):  
Hui Xue Lao
Keyword(s):  
Exponential Sums ◽  
Cusp Forms ◽  
Exponential Sums Over Primes

Short cubic exponential sums over primes

2017 ◽  
Vol 296 (1) ◽  
pp. 211-233
Author(s):  
Z. Kh. Rakhmonov ◽  
F. Z. Rakhmonov
Keyword(s):  
Exponential Sums ◽  
Exponential Sums Over Primes

Exponential sums twisted by Fourier coefficients of automorphic cusp forms for SL(2, ℤ)

2014 ◽  
Vol 11 (01) ◽  
pp. 39-49 ◽  
Author(s):  
Bin Wei
Keyword(s):  
Asymptotic Expansion ◽  
Cusp Form ◽  
Rational Number ◽  
Fourier Coefficients ◽  
Bessel Functions ◽  
Exponential Sums ◽  
Summation Formula ◽  
Cusp Forms ◽  
Real Numbers ◽  
Voronoi Summation

Let f be a holomorphic cusp form of weight k for SL(2, ℤ) with Fourier coefficients λf(n). We study the sum ∑n>0λf(n)ϕ(n/X)e(αn), where [Formula: see text]. It is proved that the sum is rapidly decaying for α close to a rational number a/q where q2 < X1-ε. The main techniques used in this paper include Dirichlet's rational approximation of real numbers, a Voronoi summation formula for SL(2, ℤ) and the asymptotic expansion for Bessel functions.

scholarly journals On certain exponential sums over primes

2009 ◽  
Vol 129 (7) ◽  
pp. 1669-1677 ◽  
Author(s):  
H. Maier ◽  
A. Sankaranarayanan
Keyword(s):  
Exponential Sums ◽  
Exponential Sums Over Primes

ON THE ERROR TERM IN THE APPROXIMATE FUNCTIONAL EQUATION FOR EXPONENTIAL SUMS RELATED TO CUSP FORMS

2008 ◽  
Vol 04 (05) ◽  
pp. 747-756 ◽  
Author(s):  
ANNE-MARIA ERNVALL-HYTÖNEN
Keyword(s):  
Functional Equation ◽  
Upper Bound ◽  
Error Term ◽  
Exponential Sums ◽  
Cusp Forms ◽  
Approximate Functional Equation ◽  
Holomorphic Cusp Forms

We give a proof for the approximate functional equation for exponential sums related to holomorphic cusp forms and derive an upper bound for the error term.

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