Transformation formulae for Dirichlet polynomials

DOI10.1016/0022-314X(84)90049-0zbMath0533.10034MaRDI QIDQ789433

Matti Jutila

Publication date: 1984

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

asymptotic behaviourRiemann zeta-functionDirichlet polynomialsmean squareVoronoi summation formuladifferences between consecutive zeros on the critical lineFourier coefficients of a cusp formRamanujan tau-function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67)

Related Items (13)

A note on the mean value of the zeta and L-functions. IV, V ⋮ Atkinson's formula for Hardy's function ⋮ An explicit formula for the square of the Riemann zeta-function in the critical strip ⋮ Gaps between consecutive zeros of the Riemann zeta-function on the critical line ⋮ An approximate functional equation for the primitive of Hardy's function ⋮ On the mean-square of the Riemann zeta-function on the critical line ⋮ A study of the mean value of the error term in the mean square formula of the Riemann zeta-function in the critical strip \(3/4\leq \sigma <1\) ⋮ Unnamed Item ⋮ An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial ⋮ A note on the gaps between zeros of Epstein's zeta-functions on the critical line ⋮ Transformation formula for exponential sums involving Fourier coefficients of modular forms ⋮ On the mean square of the periodic zeta-function. II ⋮ A note on the approximate functional equation for \(\zeta^ 2(s)\). I,II

Cites Work

• Beiträge zur Theorie der Dirichletreihen, die Spitzenformen zugeordnet sind
• La conjecture de Weil. I
• The mean-value of the Riemann zeta function
• Identities involving the coefficients of certain Dirichlet series
• Identities Involving the Coefficients of a Class of Dirichlet Series. VII
• THE TWELFTH POWER MOMENT OF THE RIEMANN-FUNCTION
• A Brun-Titschmarsh theorem for multiplicative functions.
• LATTICE-POINT SUMMATION FORMULAE
• ON DIVISOR TRANSFORMS
• Identities Involving the Coefficients of a Class of Dirichlet Series. V
• THE APPROXIMATE FUNCTIONAL EQUATION FOR ζ²(s)
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• Unnamed Item

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