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Kumar Murty, V.
- Lacunarity of Modular Forms
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1 Department of Mathematics, University of Toronto, Toronto-M5S-1A1, CA
1 Department of Mathematics, University of Toronto, Toronto-M5S-1A1, CA
Source
The Journal of the Indian Mathematical Society, Vol 52, No 1-2 (1987), Pagination: 127-146Abstract
One of the most beautiful aspects of the theory of modular forms is the arithmetical study of their Fourier coefficients. There are many results and many more conjectures. Here we shall confine ourselves to problems having to do with the vanishing or non vanishing of these Fourier coefficients.
- The Growth of Fine Selmer groups
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Authors
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1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, Hubei 430079, CN
2 Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, CA
1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, Hubei 430079, CN
2 Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, CA
Source
Journal of the Ramanujan Mathematical Society, Vol 31, No 1 (2016), Pagination: 79–94Abstract
Let A be an abelian variety defined over a number field F. In this paper, we will investigate the growth of the p-rank of the fine Selmer group in three situations. In particular, in each of these situations, we show that there is a strong analogy between the growth of the p-rank of the fine Selmer group and the growth of the p-rank of the class groups.- The Chebotarev Density Theorem and the Pair Correlation Conjecture
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Authors
Affiliations
1 Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, CA
2 Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, CA
1 Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, CA
2 Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, CA
Source
Journal of the Ramanujan Mathematical Society, Vol 33, No 4 (2018), Pagination: 399-426Abstract
In this note, we formulate pair correlation conjectures and refine the effective version of the Chebotarev density theorem established by the first two authors. Also, we apply our result to study Artin’s primitive ischolar_main conjecture and the Lang-Trotter conjectures and obtain shaper error terms.References
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- A. C. Cojocaru, E. Fouvry and M. R. Murty, The square sieve and the Lang-Trotter conjecture, Canadian Journal of Math., 57, (2005) no. 6, 1155–1177.
- A. C. Cojocaru and M. R. Murty, Cyclicity of elliptic curves modulo p and elliptic curve analogues of Linnik’s problem, Math. Annalen, 330 (2004) no. 3, 601–625.
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