On Dirichlet series associated with cubic Gauss sums. S.J. Patterson (1978) Journal für die reine und angewandte Mathematik
On discrete mean values of Dirichlet L -functions Ertan Elma (2021) Czechoslovak Mathematical Journal Let χ be a nonprincipal Dirichlet character modulo a prime number p ⩾ 3 and let 𝔞 χ : = 1 2 ( 1 - χ ( - 1 ) ) . Define the mean value ℳ p ( - s , χ ) : = 2 p - 1 ∑ ψ ( mod p ) ψ ( - 1 ) = - 1 L ( 1 , ψ ) L ( - s , χ ψ ¯ ) ( σ : = ℜ s > 0 ) . We give an identity for ℳ p ( - s , χ ) which, in particular, shows that ℳ p ( - s , χ ) = L ( 1 - s , χ ) + 𝔞 χ 2 p s L ( 1 , χ ) ζ ( - s ) + o ( 1 ) ( p → ∞ ) for fixed 0 < σ < 1 2 and | t : = ℑ s | = o ( p ( 1 - 2 σ ) / ( 3 + 2 σ ) ) .
On Eisenstein series with characters and the values of Dirichlet L-functions Bruce Berndt (1975) Acta Arithmetica
On Epstein's Zeta-function. S. Chowla, A. Selberg (1967) Journal für die reine und angewandte Mathematik
On evaluations of infinite double sums and Tornheim's double series. Kuba, Markus (2007) Séminaire Lotharingien de Combinatoire [electronic only]
On families of counting functions of number fields and hyperbolic manifolds of dimensions two and three Jay Jorgenson (1999) Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function. Karl Dilcher (1994) Aequationes mathematicae
On gigantic density of zeros of some signals defined by prime numbers Ján Mozer (1995) Czechoslovak Mathematical Journal
On Hecke L -functions associated with cusp forms. II: On the sign changes of S f ( T ) . Sankaranarayanan, A. (2006) Annales Academiae Scientiarum Fennicae. Mathematica
On hypergeometric-type generating relations associated with the generalized zeta function. Bin-Saad, M.G., Al-Gonah, A.A. (2006) Acta Mathematica Universitatis Comenianae. New Series
On Kronecker's limit formula for Dirichlet series with periodic coefficients Takeo Funakura (1990) Acta Arithmetica