Beiträge zur Theorie der Dirichletreihen, die Spitzenformen zugeordnet sind

DOI10.1016/0022-314X(81)90028-7zbMath0446.10022MaRDI QIDQ1145716

Anton Good

Publication date: 1981

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

zbMATH Keywords

Dirichlet seriescusp formsapproximate functional equationstrong mean value theorem

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11)

Related Items (33)

The square mean of Dirichlet series associated with cusp forms ⋮ A note on the mean value of the zeta and \(L\)-functions. XIV ⋮ On the analytic continuation of certain Poincaré series of elliptic modular groups ⋮ Oscillations of Hecke eigenvalues at shifted primes ⋮ SPECIAL VALUES OF SHIFTED CONVOLUTION DIRICHLET SERIES ⋮ Moments of the Riemann zeta function and Eisenstein series. II ⋮ Nonhomogeneous Rankin convolutions ⋮ Prime geodesics and averages of the Zagier L-series ⋮ Cusp forms and eigenfunctions of the Laplacian ⋮ Multiple Dirichlet series and shifted convolutions ⋮ Triple correlation sums of coefficients of cuspidal forms ⋮ Hybrid bounds for twisted L-functions ⋮ General L-functions ⋮ Mean values of certain zeta-functions on the critical line ⋮ On various means involving the Fourier coefficients of cusp forms ⋮ Explicit estimates in the arithmetic theory of cusp forms and Poincaré sets ⋮ Zeros on the critical line for Dirichlet series attached to certain cusp forms ⋮ The spectral decomposition of shifted convolution sums ⋮ The spectral decomposition of shifted convolution sums over number fields ⋮ On fractional power moments of \(L\)-functions associated with certain cusp forms ⋮ Sums of the additive divisor problem type and the inner product method ⋮ Twisted \(L\)-functions over number fields and Hilbert's eleventh problem ⋮ On fractional power moments of zeta-functions associated with certain cusp forms ⋮ The fourth power moment of automorphic $L$-functions for $GL(2)$ over a short interval ⋮ EPSTEIN ZETA-FUNCTIONS, SUBCONVEXITY, AND THE PURITY CONJECTURE ⋮ Exponential sums over primes formed with coefficients of primitive cusp forms ⋮ Oscillations of coefficients of primitive cusp forms over some special sequences ⋮ On the zeros of Dirichlet series associated with certain cusp forms ⋮ Transformation formulae for Dirichlet polynomials ⋮ Mean value of the Hecke series associated with the cusp forms of weight zero ⋮ Convolution of the Fourier coefficients of the Eisenstein-Maass series ⋮ Zeros of L-functions attached to Maass forms ⋮ Rankin-Selberg method for real analytic cusp forms of arbitrary real weight

Cites Work

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• Analytische Fortsetzung der Eisensteinreihen zu den parabolischen Spitzen von Grenzkreisgruppen erster Art
• Approximative Funktionalgleichungen und Mittelwertsätze für Dirichletreihen, die Spitzenformen assoziiert sind
• Über das quadratische Mittel der Riemannschen Zetafunktion auf der kritischen Linie
• Ein \(\Omega\)-Resultat für das quadratische Mittel der Riemannschen Zetafunktion auf der kritischen Linie
• Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung. I
• Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen. (On a new type of nonanalytic automorphic functions and the determination of Dirichlet series by functional equations)
• The mean-value of the Riemann zeta function
• An Improvement on a Theorem of Titchmarsh on the Mean Square of |ζ(12+it)|
• The Fourth Power Moment of the Riemann Zeta Function
• Primes in arithmetic progressions

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