Overview of the Work of Kumar Murty

DOI10.1007/978-3-319-97379-1_1zbMath1475.11003OpenAlexW2891167183MaRDI QIDQ5014815

Amir Akbary, M. Ram Murty, Sanoli Gun

Publication date: 8 December 2021

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-97379-1_1

Mathematics Subject Classification ID

Biographies, obituaries, personalia, bibliographies (01A70) Abelian varieties of dimension (> 1) (11G10) History of number theory (11-03) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Applications of sieve methods (11N36) Density theorems (11R45) History of algebraic geometry (14-03) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Cites Work

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• The distribution of Euler-Kronecker constants of quadratic fields
• A variant of Lehmer's conjecture
• Reductions of points on elliptic curves
• Algebraic cycles of abelian varieties
• Exceptional Hodge classes on certain abelian varieties
• Period relations and the Tate conjecture for Hilbert modular surfaces
• Mean values of derivatives of modular \(L\)-series
• Some effective cases of the Brauer-Siegel theorem
• Stark zeros in certain towers of fields
• Elliptic minuscule pairs and splitting abelian varieties
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• Lefschetz classes on abelian varieties
• Splitting of abelian varieties
• A remark on the Sato-Tate conjecture
• Nonvanishing theorems for L-functions of modular forms and their derivatives
• Some Remarks on Automorphy and the Sato-Tate Conjecture
• On the Euler Kronecker Constant of a Cyclotomic Field, II
• Zeros and poles of Artin L-series
• Splitting of Abelian Varieties
• On the logarithmic derivatives of Dirichlet L-functions at s=1
• Hodge Classes on Certain Types of Abelian Varieties
• Modular Forms and the Chebotarev Density Theorem
• Selberg’s conjectures and Artin 𝐿-functions
• Linear algebra algorithms for divisors on an algebraic curve
• OMEGA THEOREMS FOR $\frac{L'}{L}(1, \chi_D)$
• The Lindelöf class of L-functions II
• Tate Cycles on Abelian Varieties with Complex Multiplication
• Heilbronn characters
• Zeros of Dirichlet $L$-functions
• A Variant of Lehmer’s Conjecture, II: The CM-case
• Values of the Euler 𝜙-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields
• On the Euler-Kronecker constants of global fields and primes with small norms
• Improvement of a Theorem of Linnik and Walfisz
• Periods of Hilbert modular surfaces
• Non-vanishing of \(L\)-functions and applications
• The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros

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