2022/04/25 by Kieran Child, Child, Kieran
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2204.11761
openalex publication_date 2022/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a method for certifying the existence of an arbitrary Maass cusp form for any level and character. This is accomplished by producing a bound on the difference between the Δ-eigenvalue of an authentic Maass cusp form and a purported approximation of a Δ-eigenvalue, arrived at by any means. We apply this method to a proposed non-CM level 5 form with quadratic character, to present the first certified Δ-eigenvalue of such a form. This work generalises the method for certifying level 1 forms presented by Booker, Strömbergsson and Venkatesh, and is motivated by the production of purported Maass cusp forms of arbitrary level and character via methods developed by Hejhal and Strömberg.