Results 41 to 50 of about 508 (172)
L${L}$‐functions of Kloosterman sheaves
Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.Abstract In this article, we study a family of motives Mn+1k$\mathrm{M}_{n+1}^k$ associated with the symmetric power of Kloosterman sheaves constructed by Fresán, Sabbah, and Yu. They demonstrated that for n=1$n=1$, the L$L$‐functions of M2k$\mathrm{M}_{2}^k$ extend meromorphically to C$\mathbb {C}$ and satisfy the functional equations conjectured by ...
Yichen Qin
wiley +1 more source
Automorphic Representations of $GL_n$ and their $L$ functions, a talk by Shuichiro Takeda [PDF]
, 2012 The concept of automorphic representations, which can be considered as a huge generalization of classical modular forms, are one of the central themes of modern number theory known as the Langlands program.
Hundley, Joseph, Takeda, Shuichiro
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The Bruinier--Funke pairing and the orthogonal complement of unary theta functions [PDF]
, 2016 We describe an algorithm for computing the inner product between a holomorphic modular form and a unary theta function, in order to determine whether the form is orthogonal to unary theta functions without needing a basis of the entire space of modular ...
Man, SH, Kane, BR
core
, 1977 This book provides an introduction to the theory of elliptic modular functions and forms, a subject of increasing interest because of its connexions with the theory of elliptic curves.
Robert A. Rankin
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ON GENUINE CHARACTERS OF THE METAPLECTIC GROUP OF SL$_{2}$$(mathfrak{o})$ AND THETA FUNCTIONS (Automorphic forms, Automorphic representations, Galois representations, and its related topics) [PDF]
, 2021 This is a write up based on the author's talk given at the RIMS conference "Automorphic forms, Automorphic representations, Galois representations, and its related topics". Let F be a totally real number field and o the ring of integers of F.
野口, 博史
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Octonionic Magical Supergravity, Niemeier Lattices, and Exceptional & Hilbert Modular Forms
Fortschritte der Physik, Volume 72, Issue 2, February 2024.Abstract The quantum degeneracies of Bogomolny‐Prasad‐Sommerfield (BPS) black holes of octonionic magical supergravity in five dimensions are studied. Quantum degeneracy is defined purely number theoretically as the number of distinct states in charge space with a given set of invariant labels.
Murat Günaydin, Abhiram Kidambi
wiley +1 more source
A p$p$‐adic approach to the existence of level‐raising congruences
Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.Abstract We construct level‐raising congruences between p$p$‐ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the nth$n\text{th}$ symmetric power lift of a Hilbert modular eigenform of regular weight for each odd integer n=1,3,⋯,25$n =
Jack A. Thorne
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New results on automorphic integrals and their period functions
, 1987 Automorphic integrals, being generalizations of automorphic forms on discrete subgroups of S L ( 2 , R ) SL(2,\,\mathbf {R}) , share properties similar to those of ...
Richard A. Cavaliere
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Adelic Rogers integral formula
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract We formulate and prove the extension of the Rogers integral formula (Rogers [Acta Math. 94 (1955), 249–287]) to the adeles of number fields. We also prove the second moment formulas for a few important cases, enabling a number of classical and recent applications of the formula to extend immediately to any number field.
Seungki Kim
wiley +1 more source
On Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms [PDF]
, 2023 We prove an automorphic analogue of Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms. We extend the result of Morimoto based on generalization and refinement of the results of Grobner and Lin to cohomological irreducible ...
Chen, Shih-Yu
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