A note on Schwartz functions and modular forms
Sign Up to like & getrecommendations! Published in 2019 at "Archiv der Mathematik"
DOI: 10.1007/s00013-020-01459-y
Abstract: We generalize the recent work of Viazovska by constructing infinite families of Schwartz functions, suitable for Cohn–Elkies style linear programming bounds, using quasi-modular and modular forms. In particular, for dimensions $$d \equiv 0 \pmod {8}$$… read more here.
Keywords: schwartz functions; note schwartz; modular forms; functions modular ... See more keywords
Orthogonal Eisenstein series at harmonic points and modular forms of singular weight
Sign Up to like & getrecommendations! Published in 2022 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-022-03011-w
Abstract: We investigate the behaviour of orthogonal non-holomorphic Eisenstein series at their harmonic points by using theta lifts. In the case of singular weight, we show that the orthogonal non-holomorphic Eisenstein series that can be written… read more here.
Keywords: modular forms; eisenstein series; series; series harmonic ... See more keywords
Symbolic Computation for Rankin-Cohen Differential Algebras: A Case Study
Sign Up to like & getrecommendations! Published in 2017 at "Mathematics in Computer Science"
DOI: 10.1007/s11786-017-0318-0
Abstract: Don Zagier defined a “Rankin-Cohen algebra”, motivated by the study of differential operators that send modular forms to modular forms. We devised an algorithm that computes the result of the differentiation given by the modular… read more here.
Keywords: symbolic computation; rankin cohen; computation rankin; cohen differential ... See more keywords
$$C_2$$ C 2 -equivariant topological modular forms
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Homotopy and Related Structures"
DOI: 10.1007/s40062-021-00297-1
Abstract: We compute the homotopy groups of the $$C_2$$ C 2 fixed points of equivariant topological modular forms at the prime 2 using the descent spectral sequence. We then show that as a $${\mathrm {TMF}}$$ TMF… read more here.
Keywords: topological modular; equivariant topological; modular forms;
Interlacing of zeros of certain weakly holomorphic modular forms for Γ0+(2)
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2016.12.014
Abstract: Abstract We prove that zeros of each basis element of the space of weakly holomorphic modular forms of weight k for the Fricke group Γ 0 + ( 2 ) of level 2 interlace, extending… read more here.
Keywords: interlacing zeros; zeros certain; modular forms; holomorphic modular ... See more keywords
On the reduction modulo p of certain modular p-adic Galois representations
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2016.09.003
Abstract: Abstract We determine the possible Serre weights associated to certain Hilbert modular forms when the rational prime p is totally ramified in the totally real field F. Our weight lowering method for arbitrarily large weight… read more here.
Keywords: reduction; certain modular; modular adic; reduction modulo ... See more keywords
On Drinfeld modular forms of higher rank III: The analogue of the k/12-formula
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2018.04.018
Abstract: Continuing the work of \cite{7} and \cite{8}, we derive an analogue of the classical "$k/12$-formula" for Drinfeld modular forms of rank $r \geq 2$. Here the vanishing order $\nu_{\omega}(f)$ of one modular form at some… read more here.
Keywords: forms higher; analogue; drinfeld modular; modular forms ... See more keywords
Independence between coefficients of two modular forms
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2019.01.005
Abstract: Let $k$ be an even integer and $S_k$ be the space of cusp forms of weight $k$ on $\SL_2(\ZZ)$. Let $S = \oplus_{k\in 2\ZZ} S_k$. For $f, g\in S$, we let $R(f, g) = \{… read more here.
Keywords: coefficients two; two modular; modular forms; independence coefficients ... See more keywords
Algebraicity of metaplectic L-functions
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2020.09.015
Abstract: Notable results on the special values of $L$-functions of Siegel modular forms were obtained by J. Sturm in the case when the degree $n$ is even and the weight $k$ is an integer. In this… read more here.
Keywords: modular forms; method; metaplectic functions; algebraicity metaplectic ... See more keywords
ON FINE SELMER GROUPS AND SIGNED SELMER GROUPS OF ELLIPTIC MODULAR FORMS
Sign Up to like & getrecommendations! Published in 2022 at "Bulletin of the Australian Mathematical Society"
DOI: 10.1017/s0004972721000976
Abstract: Let f be an elliptic modular form and p an odd prime that is coprime to the level of f. We study the link between divisors of the characteristic ideal of the p-primary fine Selmer… read more here.
Keywords: fine selmer; elliptic modular; modular forms; selmer ... See more keywords
Half-integral weight modular forms and application to neutrino mass models
Sign Up to like & getrecommendations! Published in 2020 at "Physical Review D"
DOI: 10.1103/physrevd.102.115035
Abstract: We generalize the modular invariance approach to include the half-integral weight modular forms. Accordingly the modular group should be extended to its metaplectic covering group for consistency. We introduce the well-defined half-integral weight modular forms… read more here.
Keywords: integral weight; modular forms; weight modular; half integral ... See more keywords