On an analogue of the Sato conjecture

DOI10.1007/BF01425416zbMath0292.14011WikidataQ123352238 ScholiaQ123352238MaRDI QIDQ1211551

Hiroyuki Yoshida

Publication date: 1973

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142197

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Zeta functions and (L)-functions of number fields (11R42)

Related Items (17)

On the Sato-Tate conjecture for QM-curves of genus two ⋮ Sato–Tate distributions and Galois endomorphism modules in genus 2 ⋮ Lang–Trotter revisited ⋮ Arithmetic modeling of random processes and \(r\)-algorithms ⋮ Applications of the theory of modular forms to number theory ⋮ The distribution of the number of points modulo an integer on elliptic curves over finite fields ⋮ Methods for justifying arithmetic hypotheses and computer algebra ⋮ Distribution of the weights of the dual of the Melas code ⋮ The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields ⋮ Artin-Schreier curves, exponential sums, and coding theory ⋮ Arithmetic applications of the Langlands program ⋮ Explicit bounds and heuristics on class numbers in hyperelliptic function fields ⋮ Exponential sums over finite fields and differential equations over the complex numbers: Some interactions ⋮ Computational experiments in arithmetic geometry over finite fields and their computer support ⋮ Examples of genuine QM abelian surfaces which are modular ⋮ Distribution of Hecke eigenvalues ⋮ Distribution properties of certain exponential sums

Cites Work

• On analytic families of polarized abelian varieties and automorphic functions
• Endomorphisms of Abelian varieties over finite fields
• On the zeta function of a fibre variety whose fibres are abelian varieties
• Hecke polynomials as congruence \(\zeta\) functions in elliptic modular case
• On Ihara's modular group
• Hecke polynomials of modular groups and congruence zeta functions of fibre varieties
• Die Typen der Multiplikatorenringe elliptischer Funktionenkörper
• How the Number of Points of An Elliptic Curve Over a Fixed Prime Field Varies
• ON THE DIOPHANTINE EQUATION 4/n=1/x+1/y+1/z
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