Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection

Kane, Ben; Pujahari, Sudhir

doi:10.48550/arxiv.2010.15325

Cited by 2 publications

(2 citation statements)

References 25 publications

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“…Theorem 4.1 is a refinement of a classical theorem of Birch [4, Theorem 1] (when restricted to Legendre normal elliptic curves) that established even moments of all elliptic curves over finite fields. Recently Bringmann, Kane, and the first author [14,5] have refined Birch's result to arithmetic progressions.…”

Section: Proofs Of Theoremsmentioning

confidence: 99%

Sato-Tate Distribution of $p$-adic hypergeometric functions

Pujahari¹,

Saikia²

2022

Preprint

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Recently Ono, Saad and the second author [21] initiated a study of value distribution of certain families of Gaussian hypergeometric functions over large finite fields. They investigated two families of Gaussian hypergeometric functions and showed that they satisfy semicircular and Batman distributions. Motivated by their results we aim to study distributions of certain families of hypergeometric functions in the p-adic setting over large finite fields. In particular, we consider two and six parameters families of hypergeometric functions in the p-adic setting and obtain that their limiting distributions are semicircular over large finite fields. In the process of doing this we also express the traces of pth Hecke operators acting on the spaces of cusp forms of even weight k ≥ 4 and levels 4 and 8 in terms of p-adic hypergeometric function which is of independent interest. These results can be viewed as p-adic analogous of some trace formulas of [1,2,6].

show abstract

Section: Proofs Of Theoremsmentioning

confidence: 99%

Sato-Tate Distribution of $p$-adic hypergeometric functions

Pujahari¹,

Saikia²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Theorem 4.1 is a refinement of a classical theorem of Birch [4, Theorem 1] (when restricted to Legendre normal elliptic curves) that established even moments of all elliptic curves over finite fields. Recently Bringmann, Kane, and the first author [5,14] have refined Birch's result to arithmetic progressions. (2) p 1 3…”

Section: Theorem 41 Let M Be a Fixed Positive Integer And P > 3 Be A ...mentioning

confidence: 99%

Sato-Tate distribution of p-adic hypergeometric functions

Pujahari

Saikia

2022

Res. number theory

View full text Add to dashboard Cite

Recently Ono, Saad and the second author [21] initiated a study of value distribution of certain families of Gaussian hypergeometric functions over large finite fields. They investigated two families of Gaussian hypergeometric functions and showed that they satisfy semicircular and Batman distributions. Motivated by their results we aim to study distributions of certain families of hypergeometric functions in the p-adic setting over large finite fields. In particular, we consider two and six parameters families of hypergeometric functions in the p-adic setting and obtain that their limiting distributions are semicircular over large finite fields. In the process of doing this we also express the traces of pth Hecke operators acting on the spaces of cusp forms of even weight $$k\ge 4$$ k ≥ 4 and levels 4 and 8 in terms of p-adic hypergeometric function which is of independent interest. These results can be viewed as p-adic analogous of some trace formulas of [1, 2, 6].

show abstract

Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection

Cited by 2 publications

References 25 publications

Sato-Tate Distribution of $p$-adic hypergeometric functions

Sato-Tate Distribution of $p$-adic hypergeometric functions

Sato-Tate distribution of p-adic hypergeometric functions

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