Non-vanishing of \(L\)-functions and applications

DOI10.1007/978-3-0348-0274-1zbMath1235.11086OpenAlexW1488588695MaRDI QIDQ5894368

M. Ram Murty, V. Kumar Murty

Publication date: 30 November 2011

Published in: Modern Birkhäuser Classics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0274-1

zbMATH Keywords

prime number theoremRiemann zeta-functionmodular forms and Dirichlet seriesquadratic twists of modular \(L\)-functionsSelberg class of functions

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Zeta functions and (L)-functions of number fields (11R42) Density theorems (11R45)

Related Items (21)

ON THE ANALYTIC CONTINUATION AND NON-VANISHING OF L-FUNCTIONS ⋮ Joint value-distribution of \(L\)-functions and discrepancy of Hecke eigenvalues ⋮ RUELLE TYPE ZETA FUNCTIONS FOR TORI AND SOME ARITHMETICS ⋮ Mertens’ theorem for Chebotarev sets ⋮ A BOMBIERI–VINOGRADOV THEOREM FOR NUMBER FIELDS ⋮ Darmon cycles and the Kohnen-Shintani lifting ⋮ Quadratic Chabauty for (bi)elliptic curves and Kim's conjecture ⋮ RUELLE TYPE L-FUNCTIONS VERSUS DETERMINANTS OF LAPLACIANS FOR TORSION FREE ABELIAN GROUPS ⋮ Sato-Tate distributions ⋮ Arbitrarily long gaps between the values of positive‐definite cubic and biquadratic diagonal forms ⋮ On a theorem of Bertolini-Darmon on the rationality of Stark-Heegner points over genus fields of real quadratic fields ⋮ Upper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields ⋮ A problem of Chowla revisited ⋮ Geometric non-vanishing ⋮ The zeros of Dedekind zeta functions and class numbers of CM-fields ⋮ Chebyshev's bias in dihedral and generalized quaternion Galois groups ⋮ Level aspect of simultaneous nonvanishing for the central 𝐿-values associated to cusp forms ⋮ On a convolution series attached to a Siegel Hecke cusp form of degree 2 ⋮ On Artin L-Functions for Octic Quaternion Fields ⋮ A VARIANT OF THE BARBAN–DAVENPORT– HALBERSTAM THEOREM ⋮ GENERALIZATION OF THE EFFECTIVE WIENER–IKEHARA THEOREM

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