L-functions and division towers

DOI10.1007/BF01456842zbMath0656.14013OpenAlexW2082027267MaRDI QIDQ1109839

David E. Rohrlich

Publication date: 1988

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164442

zbMATH Keywords

conjecture of Birch and Swinnerton-DyerHecke L-functionvanishing of L

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10)

Related Items

On \(p\)-adic \(L\)-function associated with cusp forms on \(\mathrm{GL}_2\) ⋮ The critical order of vanishing of automorphic \(L\)-functions with large level ⋮ Congruences between Ramanujan's tau function and elliptic curves, and Mazur-Tate elements at additive primes ⋮ Mordell–Weil ranks and Tate–Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions ⋮ On the main conjecture of Iwasawa theory for imaginary quadratic fields ⋮ Nonvanishing of \(L\)-functions for \(\mathrm{GL}(2)\) ⋮ Congruences modulo $p$ between $\rho $-twisted Hasse-Weil $L$-values ⋮ Quadratic modular symbols on Shimura curves ⋮ Existential definability and diophantine stability ⋮ Weak Leopoldt's conjecture for Hecke characters of imaginary quadratic fields ⋮ Iwasawa theory for modular forms at supersingular primes ⋮ Ranks of Abelian varieties over infinite extensions of the rationals ⋮ The cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplication ⋮ Upper triangular operators and \(p\)-adic \(L\)-functions ⋮ On the order of vanishing of modular $L$-functions at the critical point ⋮ Anticyclotomic \(p\)-ordinary Iwasawa theory of elliptic modular forms ⋮ The exceptional zero conjecture for Hilbert modular forms ⋮ Remarks on Kato's Euler systems for elliptic curves with additive reduction ⋮ Arithmetic statistics and noncommutative Iwasawa theory ⋮ Heegner points and Beilinson-Kato elements: a conjecture of Perrin-Riou ⋮ Iwasawa theory for \(\mathrm{GL}_2\times \mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1\) ⋮ An analogue of Kida's formula for the \(p\)-adic \(L\)-functions of modular elliptic curves ⋮ An analogue of the Washington-Sinnott theorem for elliptic curves with complex multiplication I ⋮ Algebraic structure and characteristic ideals of fine Mordell-Weil groups and plus/minus Mordell-Weil groups ⋮ General Selmer groups and critical values of Hecke \(L\)-functions

Cites Work

• Unnamed Item
• On the critical values of Hecke \(L\)-functions for imaginary quadratic fields
• On \(L\)-functions of elliptic curves and cyclotomic towers
• Incomplete Kloosterman sums and a divisor problem. Appendix: On some exponential sums by Bryan J. Birch and Enrico Bombieri
• A p-adic measure attached to the zeta functions associated with two elliptic modular forms. I
• Algebraic cycles and values of L-functions. II
• Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer
• Automorphic forms on GL (2)
• On some results of Atkin and Lehner
• Algebraic cycles and values of L-functions.
• An Asymptotic Formula in the Theory of Numbers
• The divisor function $d_3(n)$ in arithmetic progressions
• The special values of the zeta functions associated with cusp forms
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• On the Birch and Swinnerton-Dyer conjecture