Journal: The Ramanujan Journal

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Publisher

Springer

Journal Volumes

ISSN

1382-4090
1572-9303

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2015 - 201932020 - 20242
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Publications 1 - 5 of 5
  • Supnorm of an eigenfunction of finitely many Hecke operators
    Item type: Journal Article
    Jana, Subhajit (2019)
    The Ramanujan Journal
  • On the representation of the number of integral points of an elliptic curve modulo a prime number
    Item type: Journal Article
    Rassias, Michael T. (2015)
    The Ramanujan Journal
    In this paper we shall investigate the problem of the representation of the number of integral points of an elliptic curve modulo a prime number p. We present a way of expressing an exponential sum which involves polynomials of third degree, in explicit non-exponential terms. In the process, we prove explicit formulas for the calculation of certain series involving the Riemann zeta function.
  • Regularized inner products of modular functions
    Item type: Journal Article
    Duke, William; Imamoglu, Özlem; Tóth, Árpád (2016)
    The Ramanujan Journal
  • Cycle integrals of meromorphic modular forms and Siegel theta functions
    Item type: Journal Article
    Schwagenscheidt, Markus (2024)
    The Ramanujan Journal
    We study meromorphic modular forms associated with positive definite binary quadratic forms and their cycle integrals along closed geodesics in the modular curve. We show that suitable linear combinations of these meromorphic modular forms have rational cycle integrals. Along the way we evaluate the cycle integrals of the Siegel theta function associated with an even lattice of signature (1, 2) in terms of Hecke's indefinite theta functions.
  • Small diameters and generators for arithmetic lattices in SL₂(R) and certain Ramanujan graphs
    Item type: Journal Article
    Steiner, Raphael (2023)
    The Ramanujan Journal
    We show that arithmetic lattices in SL₂(R), stemming from the proper units of an Eichler order in an indefinite quaternion algebra over Q, admit a 'small' covering set. In particular, we give bounds on the diameter if the quotient space is co-compact. Consequently, we show that these lattices admit small generators. Our techniques also apply to definite quaternion algebras where we show Ramanujan-strength bounds on the diameter of certain Ramanujan graphs without the use of the Ramanujan bound.
Publications 1 - 5 of 5